I am done

rl/Lib/site-packages/sympy/parsing/autolev/test-examples/README.txt

@@ -0,0 +1,9 @@
+# parsing/tests/test_autolev.py uses the .al files in this directory as inputs and checks
+# the equivalence of the parser generated codes and the respective .py files.
+
+# By default, this directory contains tests for all rules of the parser.
+
+# Additional tests consisting of full physics examples shall be made available soon in
+# the form of another repository. One shall be able to copy the contents of that repo
+# to this folder and use those tests after uncommenting the respective code in
+# parsing/tests/test_autolev.py.

rl/Lib/site-packages/sympy/parsing/autolev/test-examples/pydy-example-repo/chaos_pendulum.al

@@ -0,0 +1,33 @@
+CONSTANTS G,LB,W,H
+MOTIONVARIABLES' THETA'',PHI'',OMEGA',ALPHA'
+NEWTONIAN N
+BODIES A,B
+SIMPROT(N,A,2,THETA)
+SIMPROT(A,B,3,PHI)
+POINT O
+LA = (LB-H/2)/2
+P_O_AO> = LA*A3>
+P_O_BO> = LB*A3>
+OMEGA = THETA'
+ALPHA = PHI'
+W_A_N> = OMEGA*N2>
+W_B_A> = ALPHA*A3>
+V_O_N> = 0>
+V2PTS(N, A, O, AO)
+V2PTS(N, A, O, BO)
+MASS A=MA, B=MB
+IAXX = 1/12*MA*(2*LA)^2
+IAYY = IAXX
+IAZZ = 0
+IBXX = 1/12*MB*H^2
+IBYY = 1/12*MB*(W^2+H^2)
+IBZZ = 1/12*MB*W^2
+INERTIA A, IAXX, IAYY, IAZZ
+INERTIA B, IBXX, IBYY, IBZZ
+GRAVITY(G*N3>)
+ZERO = FR() + FRSTAR()
+KANE()
+INPUT LB=0.2,H=0.1,W=0.2,MA=0.01,MB=0.1,G=9.81
+INPUT THETA = 90 DEG, PHI = 0.5 DEG, OMEGA=0, ALPHA=0
+INPUT TFINAL=10, INTEGSTP=0.02
+CODE DYNAMICS() some_filename.c

rl/Lib/site-packages/sympy/parsing/autolev/test-examples/pydy-example-repo/chaos_pendulum.py

@@ -0,0 +1,55 @@
+import sympy.physics.mechanics as _me
+import sympy as _sm
+import math as m
+import numpy as _np
+
+g, lb, w, h = _sm.symbols('g lb w h', real=True)
+theta, phi, omega, alpha = _me.dynamicsymbols('theta phi omega alpha')
+theta_d, phi_d, omega_d, alpha_d = _me.dynamicsymbols('theta_ phi_ omega_ alpha_', 1)
+theta_dd, phi_dd = _me.dynamicsymbols('theta_ phi_', 2)
+frame_n = _me.ReferenceFrame('n')
+body_a_cm = _me.Point('a_cm')
+body_a_cm.set_vel(frame_n, 0)
+body_a_f = _me.ReferenceFrame('a_f')
+body_a = _me.RigidBody('a', body_a_cm, body_a_f, _sm.symbols('m'), (_me.outer(body_a_f.x,body_a_f.x),body_a_cm))
+body_b_cm = _me.Point('b_cm')
+body_b_cm.set_vel(frame_n, 0)
+body_b_f = _me.ReferenceFrame('b_f')
+body_b = _me.RigidBody('b', body_b_cm, body_b_f, _sm.symbols('m'), (_me.outer(body_b_f.x,body_b_f.x),body_b_cm))
+body_a_f.orient(frame_n, 'Axis', [theta, frame_n.y])
+body_b_f.orient(body_a_f, 'Axis', [phi, body_a_f.z])
+point_o = _me.Point('o')
+la = (lb-h/2)/2
+body_a_cm.set_pos(point_o, la*body_a_f.z)
+body_b_cm.set_pos(point_o, lb*body_a_f.z)
+body_a_f.set_ang_vel(frame_n, omega*frame_n.y)
+body_b_f.set_ang_vel(body_a_f, alpha*body_a_f.z)
+point_o.set_vel(frame_n, 0)
+body_a_cm.v2pt_theory(point_o,frame_n,body_a_f)
+body_b_cm.v2pt_theory(point_o,frame_n,body_a_f)
+ma = _sm.symbols('ma')
+body_a.mass = ma
+mb = _sm.symbols('mb')
+body_b.mass = mb
+iaxx = 1/12*ma*(2*la)**2
+iayy = iaxx
+iazz = 0
+ibxx = 1/12*mb*h**2
+ibyy = 1/12*mb*(w**2+h**2)
+ibzz = 1/12*mb*w**2
+body_a.inertia = (_me.inertia(body_a_f, iaxx, iayy, iazz, 0, 0, 0), body_a_cm)
+body_b.inertia = (_me.inertia(body_b_f, ibxx, ibyy, ibzz, 0, 0, 0), body_b_cm)
+force_a = body_a.mass*(g*frame_n.z)
+force_b = body_b.mass*(g*frame_n.z)
+kd_eqs = [theta_d - omega, phi_d - alpha]
+forceList = [(body_a.masscenter,body_a.mass*(g*frame_n.z)), (body_b.masscenter,body_b.mass*(g*frame_n.z))]
+kane = _me.KanesMethod(frame_n, q_ind=[theta,phi], u_ind=[omega, alpha], kd_eqs = kd_eqs)
+fr, frstar = kane.kanes_equations([body_a, body_b], forceList)
+zero = fr+frstar
+from pydy.system import System
+sys = System(kane, constants = {g:9.81, lb:0.2, w:0.2, h:0.1, ma:0.01, mb:0.1},
+specifieds={},
+initial_conditions={theta:_np.deg2rad(90), phi:_np.deg2rad(0.5), omega:0, alpha:0},
+times = _np.linspace(0.0, 10, 10/0.02))
+
+y=sys.integrate()

rl/Lib/site-packages/sympy/parsing/autolev/test-examples/pydy-example-repo/double_pendulum.al

@@ -0,0 +1,25 @@
+MOTIONVARIABLES' Q{2}', U{2}'
+CONSTANTS L,M,G
+NEWTONIAN N
+FRAMES A,B
+SIMPROT(N, A, 3, Q1)
+SIMPROT(N, B, 3, Q2)
+W_A_N>=U1*N3>
+W_B_N>=U2*N3>
+POINT O
+PARTICLES P,R
+P_O_P> = L*A1>
+P_P_R> = L*B1>
+V_O_N> = 0>
+V2PTS(N, A, O, P)
+V2PTS(N, B, P, R)
+MASS P=M, R=M
+Q1' = U1
+Q2' = U2
+GRAVITY(G*N1>)
+ZERO = FR() + FRSTAR()
+KANE()
+INPUT M=1,G=9.81,L=1
+INPUT Q1=.1,Q2=.2,U1=0,U2=0
+INPUT TFINAL=10, INTEGSTP=.01
+CODE DYNAMICS() some_filename.c

rl/Lib/site-packages/sympy/parsing/autolev/test-examples/pydy-example-repo/double_pendulum.py

@@ -0,0 +1,39 @@
+import sympy.physics.mechanics as _me
+import sympy as _sm
+import math as m
+import numpy as _np
+
+q1, q2, u1, u2 = _me.dynamicsymbols('q1 q2 u1 u2')
+q1_d, q2_d, u1_d, u2_d = _me.dynamicsymbols('q1_ q2_ u1_ u2_', 1)
+l, m, g = _sm.symbols('l m g', real=True)
+frame_n = _me.ReferenceFrame('n')
+frame_a = _me.ReferenceFrame('a')
+frame_b = _me.ReferenceFrame('b')
+frame_a.orient(frame_n, 'Axis', [q1, frame_n.z])
+frame_b.orient(frame_n, 'Axis', [q2, frame_n.z])
+frame_a.set_ang_vel(frame_n, u1*frame_n.z)
+frame_b.set_ang_vel(frame_n, u2*frame_n.z)
+point_o = _me.Point('o')
+particle_p = _me.Particle('p', _me.Point('p_pt'), _sm.Symbol('m'))
+particle_r = _me.Particle('r', _me.Point('r_pt'), _sm.Symbol('m'))
+particle_p.point.set_pos(point_o, l*frame_a.x)
+particle_r.point.set_pos(particle_p.point, l*frame_b.x)
+point_o.set_vel(frame_n, 0)
+particle_p.point.v2pt_theory(point_o,frame_n,frame_a)
+particle_r.point.v2pt_theory(particle_p.point,frame_n,frame_b)
+particle_p.mass = m
+particle_r.mass = m
+force_p = particle_p.mass*(g*frame_n.x)
+force_r = particle_r.mass*(g*frame_n.x)
+kd_eqs = [q1_d - u1, q2_d - u2]
+forceList = [(particle_p.point,particle_p.mass*(g*frame_n.x)), (particle_r.point,particle_r.mass*(g*frame_n.x))]
+kane = _me.KanesMethod(frame_n, q_ind=[q1,q2], u_ind=[u1, u2], kd_eqs = kd_eqs)
+fr, frstar = kane.kanes_equations([particle_p, particle_r], forceList)
+zero = fr+frstar
+from pydy.system import System
+sys = System(kane, constants = {l:1, m:1, g:9.81},
+specifieds={},
+initial_conditions={q1:.1, q2:.2, u1:0, u2:0},
+times = _np.linspace(0.0, 10, 10/.01))
+
+y=sys.integrate()

rl/Lib/site-packages/sympy/parsing/autolev/test-examples/pydy-example-repo/mass_spring_damper.al

@@ -0,0 +1,19 @@
+CONSTANTS M,K,B,G
+MOTIONVARIABLES' POSITION',SPEED'
+VARIABLES O
+FORCE = O*SIN(T)
+NEWTONIAN CEILING
+POINTS ORIGIN
+V_ORIGIN_CEILING> = 0>
+PARTICLES BLOCK
+P_ORIGIN_BLOCK> = POSITION*CEILING1>
+MASS BLOCK=M
+V_BLOCK_CEILING>=SPEED*CEILING1>
+POSITION' = SPEED
+FORCE_MAGNITUDE = M*G-K*POSITION-B*SPEED+FORCE
+FORCE_BLOCK>=EXPLICIT(FORCE_MAGNITUDE*CEILING1>)
+ZERO = FR() + FRSTAR()
+KANE()
+INPUT TFINAL=10.0, INTEGSTP=0.01
+INPUT M=1.0, K=1.0, B=0.2, G=9.8, POSITION=0.1, SPEED=-1.0, O=2
+CODE DYNAMICS() dummy_file.c

rl/Lib/site-packages/sympy/parsing/autolev/test-examples/pydy-example-repo/mass_spring_damper.py

@@ -0,0 +1,31 @@
+import sympy.physics.mechanics as _me
+import sympy as _sm
+import math as m
+import numpy as _np
+
+m, k, b, g = _sm.symbols('m k b g', real=True)
+position, speed = _me.dynamicsymbols('position speed')
+position_d, speed_d = _me.dynamicsymbols('position_ speed_', 1)
+o = _me.dynamicsymbols('o')
+force = o*_sm.sin(_me.dynamicsymbols._t)
+frame_ceiling = _me.ReferenceFrame('ceiling')
+point_origin = _me.Point('origin')
+point_origin.set_vel(frame_ceiling, 0)
+particle_block = _me.Particle('block', _me.Point('block_pt'), _sm.Symbol('m'))
+particle_block.point.set_pos(point_origin, position*frame_ceiling.x)
+particle_block.mass = m
+particle_block.point.set_vel(frame_ceiling, speed*frame_ceiling.x)
+force_magnitude = m*g-k*position-b*speed+force
+force_block = (force_magnitude*frame_ceiling.x).subs({position_d:speed})
+kd_eqs = [position_d - speed]
+forceList = [(particle_block.point,(force_magnitude*frame_ceiling.x).subs({position_d:speed}))]
+kane = _me.KanesMethod(frame_ceiling, q_ind=[position], u_ind=[speed], kd_eqs = kd_eqs)
+fr, frstar = kane.kanes_equations([particle_block], forceList)
+zero = fr+frstar
+from pydy.system import System
+sys = System(kane, constants = {m:1.0, k:1.0, b:0.2, g:9.8},
+specifieds={_me.dynamicsymbols('t'):lambda x, t: t, o:2},
+initial_conditions={position:0.1, speed:-1*1.0},
+times = _np.linspace(0.0, 10.0, 10.0/0.01))
+
+y=sys.integrate()

rl/Lib/site-packages/sympy/parsing/autolev/test-examples/pydy-example-repo/non_min_pendulum.al

@@ -0,0 +1,20 @@
+MOTIONVARIABLES' Q{2}''
+CONSTANTS L,M,G
+NEWTONIAN N
+POINT PN
+V_PN_N> = 0>
+THETA1 = ATAN(Q2/Q1)
+FRAMES A
+SIMPROT(N, A, 3, THETA1)
+PARTICLES P
+P_PN_P> = Q1*N1>+Q2*N2>
+MASS P=M
+V_P_N>=DT(P_P_PN>, N)
+F_V = DOT(EXPRESS(V_P_N>,A), A1>)
+GRAVITY(G*N1>)
+DEPENDENT[1] = F_V
+CONSTRAIN(DEPENDENT[Q1'])
+ZERO=FR()+FRSTAR()
+F_C = MAG(P_P_PN>)-L
+CONFIG[1]=F_C
+ZERO[2]=CONFIG[1]

rl/Lib/site-packages/sympy/parsing/autolev/test-examples/pydy-example-repo/non_min_pendulum.py

@@ -0,0 +1,36 @@
+import sympy.physics.mechanics as _me
+import sympy as _sm
+import math as m
+import numpy as _np
+
+q1, q2 = _me.dynamicsymbols('q1 q2')
+q1_d, q2_d = _me.dynamicsymbols('q1_ q2_', 1)
+q1_dd, q2_dd = _me.dynamicsymbols('q1_ q2_', 2)
+l, m, g = _sm.symbols('l m g', real=True)
+frame_n = _me.ReferenceFrame('n')
+point_pn = _me.Point('pn')
+point_pn.set_vel(frame_n, 0)
+theta1 = _sm.atan(q2/q1)
+frame_a = _me.ReferenceFrame('a')
+frame_a.orient(frame_n, 'Axis', [theta1, frame_n.z])
+particle_p = _me.Particle('p', _me.Point('p_pt'), _sm.Symbol('m'))
+particle_p.point.set_pos(point_pn, q1*frame_n.x+q2*frame_n.y)
+particle_p.mass = m
+particle_p.point.set_vel(frame_n, (point_pn.pos_from(particle_p.point)).dt(frame_n))
+f_v = _me.dot((particle_p.point.vel(frame_n)).express(frame_a), frame_a.x)
+force_p = particle_p.mass*(g*frame_n.x)
+dependent = _sm.Matrix([[0]])
+dependent[0] = f_v
+velocity_constraints = [i for i in dependent]
+u_q1_d = _me.dynamicsymbols('u_q1_d')
+u_q2_d = _me.dynamicsymbols('u_q2_d')
+kd_eqs = [q1_d-u_q1_d, q2_d-u_q2_d]
+forceList = [(particle_p.point,particle_p.mass*(g*frame_n.x))]
+kane = _me.KanesMethod(frame_n, q_ind=[q1,q2], u_ind=[u_q2_d], u_dependent=[u_q1_d], kd_eqs = kd_eqs, velocity_constraints = velocity_constraints)
+fr, frstar = kane.kanes_equations([particle_p], forceList)
+zero = fr+frstar
+f_c = point_pn.pos_from(particle_p.point).magnitude()-l
+config = _sm.Matrix([[0]])
+config[0] = f_c
+zero = zero.row_insert(zero.shape[0], _sm.Matrix([[0]]))
+zero[zero.shape[0]-1] = config[0]

rl/Lib/site-packages/sympy/parsing/autolev/test-examples/ruletest1.al

@@ -0,0 +1,8 @@
+% ruletest1.al
+CONSTANTS F = 3, G = 9.81
+CONSTANTS A, B
+CONSTANTS S, S1, S2+, S3+, S4-
+CONSTANTS K{4}, L{1:3}, P{1:2,1:3}
+CONSTANTS C{2,3}
+E1 = A*F + S2 - G
+E2 = F^2 + K3*K2*G

rl/Lib/site-packages/sympy/parsing/autolev/test-examples/ruletest1.py

@@ -0,0 +1,15 @@
+import sympy.physics.mechanics as _me
+import sympy as _sm
+import math as m
+import numpy as _np
+
+f = _sm.S(3)
+g = _sm.S(9.81)
+a, b = _sm.symbols('a b', real=True)
+s, s1 = _sm.symbols('s s1', real=True)
+s2, s3 = _sm.symbols('s2 s3', real=True, nonnegative=True)
+s4 = _sm.symbols('s4', real=True, nonpositive=True)
+k1, k2, k3, k4, l1, l2, l3, p11, p12, p13, p21, p22, p23 = _sm.symbols('k1 k2 k3 k4 l1 l2 l3 p11 p12 p13 p21 p22 p23', real=True)
+c11, c12, c13, c21, c22, c23 = _sm.symbols('c11 c12 c13 c21 c22 c23', real=True)
+e1 = a*f+s2-g
+e2 = f**2+k3*k2*g

rl/Lib/site-packages/sympy/parsing/autolev/test-examples/ruletest10.al

@@ -0,0 +1,58 @@
+% ruletest10.al
+
+VARIABLES X,Y
+COMPLEX ON
+CONSTANTS A,B
+E = A*(B*X+Y)^2
+M = [E;E]
+EXPAND(E)
+EXPAND(M)
+FACTOR(E,X)
+FACTOR(M,X)
+
+EQN[1] = A*X + B*Y
+EQN[2] = 2*A*X - 3*B*Y
+SOLVE(EQN, X, Y)
+RHS_Y = RHS(Y)
+E = (X+Y)^2 + 2*X^2
+ARRANGE(E, 2, X)
+
+CONSTANTS A,B,C
+M = [A,B;C,0]
+M2 = EVALUATE(M,A=1,B=2,C=3)
+EIG(M2, EIGVALUE, EIGVEC)
+
+NEWTONIAN N
+FRAMES A
+SIMPROT(N, A, N1>, X)
+DEGREES OFF
+SIMPROT(N, A, N1>, PI/2)
+
+CONSTANTS C{3}
+V> = C1*A1> + C2*A2> + C3*A3>
+POINTS O, P
+P_P_O> = C1*A1>
+EXPRESS(V>,N)
+EXPRESS(P_P_O>,N)
+W_A_N> = C3*A3>
+ANGVEL(A,N)
+
+V2PTS(N,A,O,P)
+PARTICLES P{2}
+V2PTS(N,A,P1,P2)
+A2PTS(N,A,P1,P)
+
+BODIES B{2}
+CONSTANT G
+GRAVITY(G*N1>)
+
+VARIABLE Z
+V> = X*A1> + Y*A3>
+P_P_O> = X*A1> + Y*A2>
+X = 2*Z
+Y = Z
+EXPLICIT(V>)
+EXPLICIT(P_P_O>)
+
+FORCE(O/P1, X*Y*A1>)
+FORCE(P2, X*Y*A1>)

rl/Lib/site-packages/sympy/parsing/autolev/test-examples/ruletest10.py

@@ -0,0 +1,64 @@
+import sympy.physics.mechanics as _me
+import sympy as _sm
+import math as m
+import numpy as _np
+
+x, y = _me.dynamicsymbols('x y')
+a, b = _sm.symbols('a b', real=True)
+e = a*(b*x+y)**2
+m = _sm.Matrix([e,e]).reshape(2, 1)
+e = e.expand()
+m = _sm.Matrix([i.expand() for i in m]).reshape((m).shape[0], (m).shape[1])
+e = _sm.factor(e, x)
+m = _sm.Matrix([_sm.factor(i,x) for i in m]).reshape((m).shape[0], (m).shape[1])
+eqn = _sm.Matrix([[0]])
+eqn[0] = a*x+b*y
+eqn = eqn.row_insert(eqn.shape[0], _sm.Matrix([[0]]))
+eqn[eqn.shape[0]-1] = 2*a*x-3*b*y
+print(_sm.solve(eqn,x,y))
+rhs_y = _sm.solve(eqn,x,y)[y]
+e = (x+y)**2+2*x**2
+e.collect(x)
+a, b, c = _sm.symbols('a b c', real=True)
+m = _sm.Matrix([a,b,c,0]).reshape(2, 2)
+m2 = _sm.Matrix([i.subs({a:1,b:2,c:3}) for i in m]).reshape((m).shape[0], (m).shape[1])
+eigvalue = _sm.Matrix([i.evalf() for i in (m2).eigenvals().keys()])
+eigvec = _sm.Matrix([i[2][0].evalf() for i in (m2).eigenvects()]).reshape(m2.shape[0], m2.shape[1])
+frame_n = _me.ReferenceFrame('n')
+frame_a = _me.ReferenceFrame('a')
+frame_a.orient(frame_n, 'Axis', [x, frame_n.x])
+frame_a.orient(frame_n, 'Axis', [_sm.pi/2, frame_n.x])
+c1, c2, c3 = _sm.symbols('c1 c2 c3', real=True)
+v = c1*frame_a.x+c2*frame_a.y+c3*frame_a.z
+point_o = _me.Point('o')
+point_p = _me.Point('p')
+point_o.set_pos(point_p, c1*frame_a.x)
+v = (v).express(frame_n)
+point_o.set_pos(point_p, (point_o.pos_from(point_p)).express(frame_n))
+frame_a.set_ang_vel(frame_n, c3*frame_a.z)
+print(frame_n.ang_vel_in(frame_a))
+point_p.v2pt_theory(point_o,frame_n,frame_a)
+particle_p1 = _me.Particle('p1', _me.Point('p1_pt'), _sm.Symbol('m'))
+particle_p2 = _me.Particle('p2', _me.Point('p2_pt'), _sm.Symbol('m'))
+particle_p2.point.v2pt_theory(particle_p1.point,frame_n,frame_a)
+point_p.a2pt_theory(particle_p1.point,frame_n,frame_a)
+body_b1_cm = _me.Point('b1_cm')
+body_b1_cm.set_vel(frame_n, 0)
+body_b1_f = _me.ReferenceFrame('b1_f')
+body_b1 = _me.RigidBody('b1', body_b1_cm, body_b1_f, _sm.symbols('m'), (_me.outer(body_b1_f.x,body_b1_f.x),body_b1_cm))
+body_b2_cm = _me.Point('b2_cm')
+body_b2_cm.set_vel(frame_n, 0)
+body_b2_f = _me.ReferenceFrame('b2_f')
+body_b2 = _me.RigidBody('b2', body_b2_cm, body_b2_f, _sm.symbols('m'), (_me.outer(body_b2_f.x,body_b2_f.x),body_b2_cm))
+g = _sm.symbols('g', real=True)
+force_p1 = particle_p1.mass*(g*frame_n.x)
+force_p2 = particle_p2.mass*(g*frame_n.x)
+force_b1 = body_b1.mass*(g*frame_n.x)
+force_b2 = body_b2.mass*(g*frame_n.x)
+z = _me.dynamicsymbols('z')
+v = x*frame_a.x+y*frame_a.z
+point_o.set_pos(point_p, x*frame_a.x+y*frame_a.y)
+v = (v).subs({x:2*z, y:z})
+point_o.set_pos(point_p, (point_o.pos_from(point_p)).subs({x:2*z, y:z}))
+force_o = -1*(x*y*frame_a.x)
+force_p1 = particle_p1.mass*(g*frame_n.x)+ x*y*frame_a.x

rl/Lib/site-packages/sympy/parsing/autolev/test-examples/ruletest11.al

@@ -0,0 +1,6 @@
+VARIABLES X, Y
+CONSTANTS A{1:2, 1:2}, B{1:2}
+EQN[1] = A11*x + A12*y - B1
+EQN[2] = A21*x + A22*y - B2
+INPUT A11=2, A12=5, A21=3, A22=4, B1=7, B2=6
+CODE ALGEBRAIC(EQN, X, Y) some_filename.c

rl/Lib/site-packages/sympy/parsing/autolev/test-examples/ruletest11.py

@@ -0,0 +1,14 @@
+import sympy.physics.mechanics as _me
+import sympy as _sm
+import math as m
+import numpy as _np
+
+x, y = _me.dynamicsymbols('x y')
+a11, a12, a21, a22, b1, b2 = _sm.symbols('a11 a12 a21 a22 b1 b2', real=True)
+eqn = _sm.Matrix([[0]])
+eqn[0] = a11*x+a12*y-b1
+eqn = eqn.row_insert(eqn.shape[0], _sm.Matrix([[0]]))
+eqn[eqn.shape[0]-1] = a21*x+a22*y-b2
+eqn_list = []
+for i in eqn:  eqn_list.append(i.subs({a11:2, a12:5, a21:3, a22:4, b1:7, b2:6}))
+print(_sm.linsolve(eqn_list, x,y))

rl/Lib/site-packages/sympy/parsing/autolev/test-examples/ruletest12.al

@@ -0,0 +1,7 @@
+VARIABLES X,Y
+CONSTANTS A,B,R
+EQN[1] = A*X^3+B*Y^2-R
+EQN[2] = A*SIN(X)^2 + B*COS(2*Y) - R^2
+INPUT A=2.0, B=3.0, R=1.0
+INPUT X = 30 DEG, Y = 3.14
+CODE NONLINEAR(EQN,X,Y) some_filename.c

rl/Lib/site-packages/sympy/parsing/autolev/test-examples/ruletest12.py

@@ -0,0 +1,14 @@
+import sympy.physics.mechanics as _me
+import sympy as _sm
+import math as m
+import numpy as _np
+
+x, y = _me.dynamicsymbols('x y')
+a, b, r = _sm.symbols('a b r', real=True)
+eqn = _sm.Matrix([[0]])
+eqn[0] = a*x**3+b*y**2-r
+eqn = eqn.row_insert(eqn.shape[0], _sm.Matrix([[0]]))
+eqn[eqn.shape[0]-1] = a*_sm.sin(x)**2+b*_sm.cos(2*y)-r**2
+matrix_list = []
+for i in eqn:matrix_list.append(i.subs({a:2.0, b:3.0, r:1.0}))
+print(_sm.nsolve(matrix_list,(x,y),(_np.deg2rad(30),3.14)))

rl/Lib/site-packages/sympy/parsing/autolev/test-examples/ruletest2.al

@@ -0,0 +1,12 @@
+% ruletest2.al
+VARIABLES X1,X2
+SPECIFIED F1 = X1*X2 + 3*X1^2
+SPECIFIED F2=X1*T+X2*T^2
+VARIABLE X', Y''
+MOTIONVARIABLES Q{3}, U{2}
+VARIABLES P{2}'
+VARIABLE W{3}', R{2}''
+VARIABLES C{1:2, 1:2}
+VARIABLES D{1,3}
+VARIABLES J{1:2}
+IMAGINARY N

rl/Lib/site-packages/sympy/parsing/autolev/test-examples/ruletest2.py

@@ -0,0 +1,22 @@
+import sympy.physics.mechanics as _me
+import sympy as _sm
+import math as m
+import numpy as _np
+
+x1, x2 = _me.dynamicsymbols('x1 x2')
+f1 = x1*x2+3*x1**2
+f2 = x1*_me.dynamicsymbols._t+x2*_me.dynamicsymbols._t**2
+x, y = _me.dynamicsymbols('x y')
+x_d, y_d = _me.dynamicsymbols('x_ y_', 1)
+y_dd = _me.dynamicsymbols('y_', 2)
+q1, q2, q3, u1, u2 = _me.dynamicsymbols('q1 q2 q3 u1 u2')
+p1, p2 = _me.dynamicsymbols('p1 p2')
+p1_d, p2_d = _me.dynamicsymbols('p1_ p2_', 1)
+w1, w2, w3, r1, r2 = _me.dynamicsymbols('w1 w2 w3 r1 r2')
+w1_d, w2_d, w3_d, r1_d, r2_d = _me.dynamicsymbols('w1_ w2_ w3_ r1_ r2_', 1)
+r1_dd, r2_dd = _me.dynamicsymbols('r1_ r2_', 2)
+c11, c12, c21, c22 = _me.dynamicsymbols('c11 c12 c21 c22')
+d11, d12, d13 = _me.dynamicsymbols('d11 d12 d13')
+j1, j2 = _me.dynamicsymbols('j1 j2')
+n = _sm.symbols('n')
+n = _sm.I

rl/Lib/site-packages/sympy/parsing/autolev/test-examples/ruletest3.al

@@ -0,0 +1,25 @@
+% ruletest3.al
+FRAMES A, B
+NEWTONIAN N
+
+VARIABLES X{3}
+CONSTANTS L
+
+V1> = X1*A1> + X2*A2> + X3*A3>
+V2> = X1*B1> + X2*B2> + X3*B3>
+V3> = X1*N1> + X2*N2> + X3*N3>
+
+V> = V1> + V2> + V3>
+
+POINTS C, D
+POINTS PO{3}
+
+PARTICLES L
+PARTICLES P{3}
+
+BODIES S
+BODIES R{2}
+
+V4> = X1*S1> + X2*S2> + X3*S3>
+
+P_C_SO> = L*N1>

rl/Lib/site-packages/sympy/parsing/autolev/test-examples/ruletest3.py

@@ -0,0 +1,37 @@
+import sympy.physics.mechanics as _me
+import sympy as _sm
+import math as m
+import numpy as _np
+
+frame_a = _me.ReferenceFrame('a')
+frame_b = _me.ReferenceFrame('b')
+frame_n = _me.ReferenceFrame('n')
+x1, x2, x3 = _me.dynamicsymbols('x1 x2 x3')
+l = _sm.symbols('l', real=True)
+v1 = x1*frame_a.x+x2*frame_a.y+x3*frame_a.z
+v2 = x1*frame_b.x+x2*frame_b.y+x3*frame_b.z
+v3 = x1*frame_n.x+x2*frame_n.y+x3*frame_n.z
+v = v1+v2+v3
+point_c = _me.Point('c')
+point_d = _me.Point('d')
+point_po1 = _me.Point('po1')
+point_po2 = _me.Point('po2')
+point_po3 = _me.Point('po3')
+particle_l = _me.Particle('l', _me.Point('l_pt'), _sm.Symbol('m'))
+particle_p1 = _me.Particle('p1', _me.Point('p1_pt'), _sm.Symbol('m'))
+particle_p2 = _me.Particle('p2', _me.Point('p2_pt'), _sm.Symbol('m'))
+particle_p3 = _me.Particle('p3', _me.Point('p3_pt'), _sm.Symbol('m'))
+body_s_cm = _me.Point('s_cm')
+body_s_cm.set_vel(frame_n, 0)
+body_s_f = _me.ReferenceFrame('s_f')
+body_s = _me.RigidBody('s', body_s_cm, body_s_f, _sm.symbols('m'), (_me.outer(body_s_f.x,body_s_f.x),body_s_cm))
+body_r1_cm = _me.Point('r1_cm')
+body_r1_cm.set_vel(frame_n, 0)
+body_r1_f = _me.ReferenceFrame('r1_f')
+body_r1 = _me.RigidBody('r1', body_r1_cm, body_r1_f, _sm.symbols('m'), (_me.outer(body_r1_f.x,body_r1_f.x),body_r1_cm))
+body_r2_cm = _me.Point('r2_cm')
+body_r2_cm.set_vel(frame_n, 0)
+body_r2_f = _me.ReferenceFrame('r2_f')
+body_r2 = _me.RigidBody('r2', body_r2_cm, body_r2_f, _sm.symbols('m'), (_me.outer(body_r2_f.x,body_r2_f.x),body_r2_cm))
+v4 = x1*body_s_f.x+x2*body_s_f.y+x3*body_s_f.z
+body_s_cm.set_pos(point_c, l*frame_n.x)

rl/Lib/site-packages/sympy/parsing/autolev/test-examples/ruletest4.al

@@ -0,0 +1,20 @@
+% ruletest4.al
+
+FRAMES A, B
+MOTIONVARIABLES Q{3}
+SIMPROT(A, B, 1, Q3)
+DCM = A_B
+M = DCM*3 - A_B
+
+VARIABLES R
+CIRCLE_AREA = PI*R^2
+
+VARIABLES U, A
+VARIABLES X, Y
+S = U*T - 1/2*A*T^2
+
+EXPR1 = 2*A*0.5 - 1.25 + 0.25
+EXPR2 = -X^2 + Y^2 + 0.25*(X+Y)^2
+EXPR3 = 0.5E-10
+
+DYADIC>> = A1>*A1> + A2>*A2> + A3>*A3>

rl/Lib/site-packages/sympy/parsing/autolev/test-examples/ruletest4.py

@@ -0,0 +1,20 @@
+import sympy.physics.mechanics as _me
+import sympy as _sm
+import math as m
+import numpy as _np
+
+frame_a = _me.ReferenceFrame('a')
+frame_b = _me.ReferenceFrame('b')
+q1, q2, q3 = _me.dynamicsymbols('q1 q2 q3')
+frame_b.orient(frame_a, 'Axis', [q3, frame_a.x])
+dcm = frame_a.dcm(frame_b)
+m = dcm*3-frame_a.dcm(frame_b)
+r = _me.dynamicsymbols('r')
+circle_area = _sm.pi*r**2
+u, a = _me.dynamicsymbols('u a')
+x, y = _me.dynamicsymbols('x y')
+s = u*_me.dynamicsymbols._t-1/2*a*_me.dynamicsymbols._t**2
+expr1 = 2*a*0.5-1.25+0.25
+expr2 = -1*x**2+y**2+0.25*(x+y)**2
+expr3 = 0.5*10**(-10)
+dyadic = _me.outer(frame_a.x, frame_a.x)+_me.outer(frame_a.y, frame_a.y)+_me.outer(frame_a.z, frame_a.z)

rl/Lib/site-packages/sympy/parsing/autolev/test-examples/ruletest5.al

@@ -0,0 +1,32 @@
+% ruletest5.al
+VARIABLES X', Y'
+
+E1 = (X+Y)^2 + (X-Y)^3
+E2 = (X-Y)^2
+E3 = X^2 + Y^2 + 2*X*Y
+
+M1 = [E1;E2]
+M2 = [(X+Y)^2,(X-Y)^2]
+M3 = M1 + [X;Y]
+
+AM = EXPAND(M1)
+CM = EXPAND([(X+Y)^2,(X-Y)^2])
+EM = EXPAND(M1 + [X;Y])
+F = EXPAND(E1)
+G = EXPAND(E2)
+
+A = FACTOR(E3, X)
+BM = FACTOR(M1, X)
+CM = FACTOR(M1 + [X;Y], X)
+
+A = D(E3, X)
+B = D(E3, Y)
+CM = D(M2, X)
+DM = D(M1 + [X;Y], X)
+FRAMES A, B
+A_B = [1,0,0;1,0,0;1,0,0]
+V1> = X*A1> + Y*A2> + X*Y*A3>
+E> = D(V1>, X, B)
+FM = DT(M1)
+GM = DT([(X+Y)^2,(X-Y)^2])
+H> = DT(V1>, B)

rl/Lib/site-packages/sympy/parsing/autolev/test-examples/ruletest5.py

@@ -0,0 +1,33 @@
+import sympy.physics.mechanics as _me
+import sympy as _sm
+import math as m
+import numpy as _np
+
+x, y = _me.dynamicsymbols('x y')
+x_d, y_d = _me.dynamicsymbols('x_ y_', 1)
+e1 = (x+y)**2+(x-y)**3
+e2 = (x-y)**2
+e3 = x**2+y**2+2*x*y
+m1 = _sm.Matrix([e1,e2]).reshape(2, 1)
+m2 = _sm.Matrix([(x+y)**2,(x-y)**2]).reshape(1, 2)
+m3 = m1+_sm.Matrix([x,y]).reshape(2, 1)
+am = _sm.Matrix([i.expand() for i in m1]).reshape((m1).shape[0], (m1).shape[1])
+cm = _sm.Matrix([i.expand() for i in _sm.Matrix([(x+y)**2,(x-y)**2]).reshape(1, 2)]).reshape((_sm.Matrix([(x+y)**2,(x-y)**2]).reshape(1, 2)).shape[0], (_sm.Matrix([(x+y)**2,(x-y)**2]).reshape(1, 2)).shape[1])
+em = _sm.Matrix([i.expand() for i in m1+_sm.Matrix([x,y]).reshape(2, 1)]).reshape((m1+_sm.Matrix([x,y]).reshape(2, 1)).shape[0], (m1+_sm.Matrix([x,y]).reshape(2, 1)).shape[1])
+f = (e1).expand()
+g = (e2).expand()
+a = _sm.factor((e3), x)
+bm = _sm.Matrix([_sm.factor(i, x) for i in m1]).reshape((m1).shape[0], (m1).shape[1])
+cm = _sm.Matrix([_sm.factor(i, x) for i in m1+_sm.Matrix([x,y]).reshape(2, 1)]).reshape((m1+_sm.Matrix([x,y]).reshape(2, 1)).shape[0], (m1+_sm.Matrix([x,y]).reshape(2, 1)).shape[1])
+a = (e3).diff(x)
+b = (e3).diff(y)
+cm = _sm.Matrix([i.diff(x) for i in m2]).reshape((m2).shape[0], (m2).shape[1])
+dm = _sm.Matrix([i.diff(x) for i in m1+_sm.Matrix([x,y]).reshape(2, 1)]).reshape((m1+_sm.Matrix([x,y]).reshape(2, 1)).shape[0], (m1+_sm.Matrix([x,y]).reshape(2, 1)).shape[1])
+frame_a = _me.ReferenceFrame('a')
+frame_b = _me.ReferenceFrame('b')
+frame_b.orient(frame_a, 'DCM', _sm.Matrix([1,0,0,1,0,0,1,0,0]).reshape(3, 3))
+v1 = x*frame_a.x+y*frame_a.y+x*y*frame_a.z
+e = (v1).diff(x, frame_b)
+fm = _sm.Matrix([i.diff(_sm.Symbol('t')) for i in m1]).reshape((m1).shape[0], (m1).shape[1])
+gm = _sm.Matrix([i.diff(_sm.Symbol('t')) for i in _sm.Matrix([(x+y)**2,(x-y)**2]).reshape(1, 2)]).reshape((_sm.Matrix([(x+y)**2,(x-y)**2]).reshape(1, 2)).shape[0], (_sm.Matrix([(x+y)**2,(x-y)**2]).reshape(1, 2)).shape[1])
+h = (v1).dt(frame_b)

rl/Lib/site-packages/sympy/parsing/autolev/test-examples/ruletest6.al

@@ -0,0 +1,41 @@
+% ruletest6.al
+VARIABLES Q{2}
+VARIABLES X,Y,Z
+Q1 = X^2 + Y^2
+Q2 = X-Y
+E = Q1 + Q2
+A = EXPLICIT(E)
+E2 = COS(X)
+E3 = COS(X*Y)
+A = TAYLOR(E2, 0:2, X=0)
+B = TAYLOR(E3, 0:2, X=0, Y=0)
+
+E = EXPAND((X+Y)^2)
+A = EVALUATE(E, X=1, Y=Z)
+BM = EVALUATE([E;2*E], X=1, Y=Z)
+
+E = Q1 + Q2
+A = EVALUATE(E, X=2, Y=Z^2)
+
+CONSTANTS J,K,L
+P1 = POLYNOMIAL([J,K,L],X)
+P2 = POLYNOMIAL(J*X+K,X,1)
+
+ROOT1 = ROOTS(P1, X, 2)
+ROOT2 = ROOTS([1;2;3])
+
+M = [1,2,3,4;5,6,7,8;9,10,11,12;13,14,15,16]
+
+AM = TRANSPOSE(M) + M
+BM = EIG(M)
+C1 = DIAGMAT(4, 1)
+C2 = DIAGMAT(3, 4, 2)
+DM = INV(M+C1)
+E = DET(M+C1) + TRACE([1,0;0,1])
+F = ELEMENT(M, 2, 3)
+
+A = COLS(M)
+BM = COLS(M, 1)
+CM = COLS(M, 1, 2:4, 3)
+DM = ROWS(M, 1)
+EM = ROWS(M, 1, 2:4, 3)

rl/Lib/site-packages/sympy/parsing/autolev/test-examples/ruletest6.py

@@ -0,0 +1,36 @@
+import sympy.physics.mechanics as _me
+import sympy as _sm
+import math as m
+import numpy as _np
+
+q1, q2 = _me.dynamicsymbols('q1 q2')
+x, y, z = _me.dynamicsymbols('x y z')
+e = q1+q2
+a = (e).subs({q1:x**2+y**2, q2:x-y})
+e2 = _sm.cos(x)
+e3 = _sm.cos(x*y)
+a = (e2).series(x, 0, 2).removeO()
+b = (e3).series(x, 0, 2).removeO().series(y, 0, 2).removeO()
+e = ((x+y)**2).expand()
+a = (e).subs({q1:x**2+y**2,q2:x-y}).subs({x:1,y:z})
+bm = _sm.Matrix([i.subs({x:1,y:z}) for i in _sm.Matrix([e,2*e]).reshape(2, 1)]).reshape((_sm.Matrix([e,2*e]).reshape(2, 1)).shape[0], (_sm.Matrix([e,2*e]).reshape(2, 1)).shape[1])
+e = q1+q2
+a = (e).subs({q1:x**2+y**2,q2:x-y}).subs({x:2,y:z**2})
+j, k, l = _sm.symbols('j k l', real=True)
+p1 = _sm.Poly(_sm.Matrix([j,k,l]).reshape(1, 3), x)
+p2 = _sm.Poly(j*x+k, x)
+root1 = [i.evalf() for i in _sm.solve(p1, x)]
+root2 = [i.evalf() for i in _sm.solve(_sm.Poly(_sm.Matrix([1,2,3]).reshape(3, 1), x),x)]
+m = _sm.Matrix([1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16]).reshape(4, 4)
+am = (m).T+m
+bm = _sm.Matrix([i.evalf() for i in (m).eigenvals().keys()])
+c1 = _sm.diag(1,1,1,1)
+c2 = _sm.Matrix([2 if i==j else 0 for i in range(3) for j in range(4)]).reshape(3, 4)
+dm = (m+c1)**(-1)
+e = (m+c1).det()+(_sm.Matrix([1,0,0,1]).reshape(2, 2)).trace()
+f = (m)[1,2]
+a = (m).cols
+bm = (m).col(0)
+cm = _sm.Matrix([(m).T.row(0),(m).T.row(1),(m).T.row(2),(m).T.row(3),(m).T.row(2)])
+dm = (m).row(0)
+em = _sm.Matrix([(m).row(0),(m).row(1),(m).row(2),(m).row(3),(m).row(2)])

rl/Lib/site-packages/sympy/parsing/autolev/test-examples/ruletest7.al

@@ -0,0 +1,39 @@
+% ruletest7.al
+VARIABLES X', Y'
+E = COS(X) + SIN(X) + TAN(X)&
++ COSH(X) + SINH(X) + TANH(X)&
++ ACOS(X) + ASIN(X) + ATAN(X)&
++ LOG(X) + EXP(X) + SQRT(X)&
++ FACTORIAL(X) + CEIL(X) +&
+FLOOR(X) + SIGN(X)
+
+E = SQR(X) + LOG10(X)
+
+A = ABS(-1) + INT(1.5) + ROUND(1.9)
+
+E1 = 2*X + 3*Y
+E2 = X + Y
+
+AM = COEF([E1;E2], [X,Y])
+B = COEF(E1, X)
+C = COEF(E2, Y)
+D1 = EXCLUDE(E1, X)
+D2 = INCLUDE(E1, X)
+FM = ARRANGE([E1,E2],2,X)
+F = ARRANGE(E1, 2, Y)
+G = REPLACE(E1, X=2*X)
+GM = REPLACE([E1;E2], X=3)
+
+FRAMES A, B
+VARIABLES THETA
+SIMPROT(A,B,3,THETA)
+V1> = 2*A1> - 3*A2> + A3>
+V2> = B1> + B2> + B3>
+A = DOT(V1>, V2>)
+BM = DOT(V1>, [V2>;2*V2>])
+C> = CROSS(V1>,V2>)
+D = MAG(2*V1>) + MAG(3*V1>)
+DYADIC>> = 3*A1>*A1> + A2>*A2> + 2*A3>*A3>
+AM = MATRIX(B, DYADIC>>)
+M = [1;2;3]
+V> = VECTOR(A, M)

rl/Lib/site-packages/sympy/parsing/autolev/test-examples/ruletest7.py

@@ -0,0 +1,35 @@
+import sympy.physics.mechanics as _me
+import sympy as _sm
+import math as m
+import numpy as _np
+
+x, y = _me.dynamicsymbols('x y')
+x_d, y_d = _me.dynamicsymbols('x_ y_', 1)
+e = _sm.cos(x)+_sm.sin(x)+_sm.tan(x)+_sm.cosh(x)+_sm.sinh(x)+_sm.tanh(x)+_sm.acos(x)+_sm.asin(x)+_sm.atan(x)+_sm.log(x)+_sm.exp(x)+_sm.sqrt(x)+_sm.factorial(x)+_sm.ceiling(x)+_sm.floor(x)+_sm.sign(x)
+e = (x)**2+_sm.log(x, 10)
+a = _sm.Abs(-1*1)+int(1.5)+round(1.9)
+e1 = 2*x+3*y
+e2 = x+y
+am = _sm.Matrix([e1.expand().coeff(x), e1.expand().coeff(y), e2.expand().coeff(x), e2.expand().coeff(y)]).reshape(2, 2)
+b = (e1).expand().coeff(x)
+c = (e2).expand().coeff(y)
+d1 = (e1).collect(x).coeff(x,0)
+d2 = (e1).collect(x).coeff(x,1)
+fm = _sm.Matrix([i.collect(x)for i in _sm.Matrix([e1,e2]).reshape(1, 2)]).reshape((_sm.Matrix([e1,e2]).reshape(1, 2)).shape[0], (_sm.Matrix([e1,e2]).reshape(1, 2)).shape[1])
+f = (e1).collect(y)
+g = (e1).subs({x:2*x})
+gm = _sm.Matrix([i.subs({x:3}) for i in _sm.Matrix([e1,e2]).reshape(2, 1)]).reshape((_sm.Matrix([e1,e2]).reshape(2, 1)).shape[0], (_sm.Matrix([e1,e2]).reshape(2, 1)).shape[1])
+frame_a = _me.ReferenceFrame('a')
+frame_b = _me.ReferenceFrame('b')
+theta = _me.dynamicsymbols('theta')
+frame_b.orient(frame_a, 'Axis', [theta, frame_a.z])
+v1 = 2*frame_a.x-3*frame_a.y+frame_a.z
+v2 = frame_b.x+frame_b.y+frame_b.z
+a = _me.dot(v1, v2)
+bm = _sm.Matrix([_me.dot(v1, v2),_me.dot(v1, 2*v2)]).reshape(2, 1)
+c = _me.cross(v1, v2)
+d = 2*v1.magnitude()+3*v1.magnitude()
+dyadic = _me.outer(3*frame_a.x, frame_a.x)+_me.outer(frame_a.y, frame_a.y)+_me.outer(2*frame_a.z, frame_a.z)
+am = (dyadic).to_matrix(frame_b)
+m = _sm.Matrix([1,2,3]).reshape(3, 1)
+v = m[0]*frame_a.x +m[1]*frame_a.y +m[2]*frame_a.z

rl/Lib/site-packages/sympy/parsing/autolev/test-examples/ruletest8.al

@@ -0,0 +1,38 @@
+% ruletest8.al
+FRAMES A
+CONSTANTS C{3}
+A>> = EXPRESS(1>>,A)
+PARTICLES P1, P2
+BODIES R
+R_A = [1,1,1;1,1,0;0,0,1]
+POINT O
+MASS P1=M1, P2=M2, R=MR
+INERTIA R, I1, I2, I3
+P_P1_O> = C1*A1>
+P_P2_O> = C2*A2>
+P_RO_O> = C3*A3>
+A>> = EXPRESS(I_P1_O>>, A)
+A>> = EXPRESS(I_P2_O>>, A)
+A>> = EXPRESS(I_R_O>>, A)
+A>> = EXPRESS(INERTIA(O), A)
+A>> = EXPRESS(INERTIA(O, P1, R), A)
+A>> = EXPRESS(I_R_O>>, A)
+A>> = EXPRESS(I_R_RO>>, A)
+
+P_P1_P2> = C1*A1> + C2*A2>
+P_P1_RO> = C3*A1>
+P_P2_RO> = C3*A2>
+
+B> = CM(O)
+B> = CM(O, P1, R)
+B> = CM(P1)
+
+MOTIONVARIABLES U{3}
+V> = U1*A1> + U2*A2> + U3*A3>
+U> = UNITVEC(V> + C1*A1>)
+V_P1_A> = U1*A1>
+A> = PARTIALS(V_P1_A>, U1)
+
+M = MASS(P1,R)
+M = MASS(P2)
+M = MASS()

rl/Lib/site-packages/sympy/parsing/autolev/test-examples/ruletest8.py

@@ -0,0 +1,49 @@
+import sympy.physics.mechanics as _me
+import sympy as _sm
+import math as m
+import numpy as _np
+
+frame_a = _me.ReferenceFrame('a')
+c1, c2, c3 = _sm.symbols('c1 c2 c3', real=True)
+a = _me.inertia(frame_a, 1, 1, 1)
+particle_p1 = _me.Particle('p1', _me.Point('p1_pt'), _sm.Symbol('m'))
+particle_p2 = _me.Particle('p2', _me.Point('p2_pt'), _sm.Symbol('m'))
+body_r_cm = _me.Point('r_cm')
+body_r_f = _me.ReferenceFrame('r_f')
+body_r = _me.RigidBody('r', body_r_cm, body_r_f, _sm.symbols('m'), (_me.outer(body_r_f.x,body_r_f.x),body_r_cm))
+frame_a.orient(body_r_f, 'DCM', _sm.Matrix([1,1,1,1,1,0,0,0,1]).reshape(3, 3))
+point_o = _me.Point('o')
+m1 = _sm.symbols('m1')
+particle_p1.mass = m1
+m2 = _sm.symbols('m2')
+particle_p2.mass = m2
+mr = _sm.symbols('mr')
+body_r.mass = mr
+i1 = _sm.symbols('i1')
+i2 = _sm.symbols('i2')
+i3 = _sm.symbols('i3')
+body_r.inertia = (_me.inertia(body_r_f, i1, i2, i3, 0, 0, 0), body_r_cm)
+point_o.set_pos(particle_p1.point, c1*frame_a.x)
+point_o.set_pos(particle_p2.point, c2*frame_a.y)
+point_o.set_pos(body_r_cm, c3*frame_a.z)
+a = _me.inertia_of_point_mass(particle_p1.mass, particle_p1.point.pos_from(point_o), frame_a)
+a = _me.inertia_of_point_mass(particle_p2.mass, particle_p2.point.pos_from(point_o), frame_a)
+a = body_r.inertia[0] + _me.inertia_of_point_mass(body_r.mass, body_r.masscenter.pos_from(point_o), frame_a)
+a = _me.inertia_of_point_mass(particle_p1.mass, particle_p1.point.pos_from(point_o), frame_a) + _me.inertia_of_point_mass(particle_p2.mass, particle_p2.point.pos_from(point_o), frame_a) + body_r.inertia[0] + _me.inertia_of_point_mass(body_r.mass, body_r.masscenter.pos_from(point_o), frame_a)
+a = _me.inertia_of_point_mass(particle_p1.mass, particle_p1.point.pos_from(point_o), frame_a) + body_r.inertia[0] + _me.inertia_of_point_mass(body_r.mass, body_r.masscenter.pos_from(point_o), frame_a)
+a = body_r.inertia[0] + _me.inertia_of_point_mass(body_r.mass, body_r.masscenter.pos_from(point_o), frame_a)
+a = body_r.inertia[0]
+particle_p2.point.set_pos(particle_p1.point, c1*frame_a.x+c2*frame_a.y)
+body_r_cm.set_pos(particle_p1.point, c3*frame_a.x)
+body_r_cm.set_pos(particle_p2.point, c3*frame_a.y)
+b = _me.functions.center_of_mass(point_o,particle_p1, particle_p2, body_r)
+b = _me.functions.center_of_mass(point_o,particle_p1, body_r)
+b = _me.functions.center_of_mass(particle_p1.point,particle_p1, particle_p2, body_r)
+u1, u2, u3 = _me.dynamicsymbols('u1 u2 u3')
+v = u1*frame_a.x+u2*frame_a.y+u3*frame_a.z
+u = (v+c1*frame_a.x).normalize()
+particle_p1.point.set_vel(frame_a, u1*frame_a.x)
+a = particle_p1.point.partial_velocity(frame_a, u1)
+m = particle_p1.mass+body_r.mass
+m = particle_p2.mass
+m = particle_p1.mass+particle_p2.mass+body_r.mass

rl/Lib/site-packages/sympy/parsing/autolev/test-examples/ruletest9.al

@@ -0,0 +1,54 @@
+% ruletest9.al
+NEWTONIAN N
+FRAMES A
+A> = 0>
+D>> = EXPRESS(1>>, A)
+
+POINTS PO{2}
+PARTICLES P{2}
+MOTIONVARIABLES' C{3}'
+BODIES R
+P_P1_PO2> = C1*A1>
+V> = 2*P_P1_PO2> + C2*A2>
+
+W_A_N> = C3*A3>
+V> = 2*W_A_N> + C2*A2>
+W_R_N> = C3*A3>
+V> = 2*W_R_N> + C2*A2>
+
+ALF_A_N> = DT(W_A_N>, A)
+V> = 2*ALF_A_N> + C2*A2>
+
+V_P1_A> = C1*A1> + C3*A2>
+A_RO_N> = C2*A2>
+V_A> = CROSS(A_RO_N>, V_P1_A>)
+
+X_B_C> = V_A>
+X_B_D> = 2*X_B_C>
+A_B_C_D_E> = X_B_D>*2
+
+A_B_C = 2*C1*C2*C3
+A_B_C += 2*C1
+A_B_C := 3*C1
+
+MOTIONVARIABLES' Q{2}', U{2}'
+Q1' = U1
+Q2' = U2
+
+VARIABLES X'', Y''
+SPECIFIED YY
+Y'' = X*X'^2 + 1
+YY = X*X'^2 + 1
+
+M[1] = 2*X
+M[2] = 2*Y
+A = 2*M[1]
+
+M = [1,2,3;4,5,6;7,8,9]
+M[1, 2] = 5
+A = M[1, 2]*2
+
+FORCE_RO> = Q1*N1>
+TORQUE_A> = Q2*N3>
+FORCE_RO> = Q2*N2>
+F> = FORCE_RO>*2

rl/Lib/site-packages/sympy/parsing/autolev/test-examples/ruletest9.py

@@ -0,0 +1,55 @@
+import sympy.physics.mechanics as _me
+import sympy as _sm
+import math as m
+import numpy as _np
+
+frame_n = _me.ReferenceFrame('n')
+frame_a = _me.ReferenceFrame('a')
+a = 0
+d = _me.inertia(frame_a, 1, 1, 1)
+point_po1 = _me.Point('po1')
+point_po2 = _me.Point('po2')
+particle_p1 = _me.Particle('p1', _me.Point('p1_pt'), _sm.Symbol('m'))
+particle_p2 = _me.Particle('p2', _me.Point('p2_pt'), _sm.Symbol('m'))
+c1, c2, c3 = _me.dynamicsymbols('c1 c2 c3')
+c1_d, c2_d, c3_d = _me.dynamicsymbols('c1_ c2_ c3_', 1)
+body_r_cm = _me.Point('r_cm')
+body_r_cm.set_vel(frame_n, 0)
+body_r_f = _me.ReferenceFrame('r_f')
+body_r = _me.RigidBody('r', body_r_cm, body_r_f, _sm.symbols('m'), (_me.outer(body_r_f.x,body_r_f.x),body_r_cm))
+point_po2.set_pos(particle_p1.point, c1*frame_a.x)
+v = 2*point_po2.pos_from(particle_p1.point)+c2*frame_a.y
+frame_a.set_ang_vel(frame_n, c3*frame_a.z)
+v = 2*frame_a.ang_vel_in(frame_n)+c2*frame_a.y
+body_r_f.set_ang_vel(frame_n, c3*frame_a.z)
+v = 2*body_r_f.ang_vel_in(frame_n)+c2*frame_a.y
+frame_a.set_ang_acc(frame_n, (frame_a.ang_vel_in(frame_n)).dt(frame_a))
+v = 2*frame_a.ang_acc_in(frame_n)+c2*frame_a.y
+particle_p1.point.set_vel(frame_a, c1*frame_a.x+c3*frame_a.y)
+body_r_cm.set_acc(frame_n, c2*frame_a.y)
+v_a = _me.cross(body_r_cm.acc(frame_n), particle_p1.point.vel(frame_a))
+x_b_c = v_a
+x_b_d = 2*x_b_c
+a_b_c_d_e = x_b_d*2
+a_b_c = 2*c1*c2*c3
+a_b_c += 2*c1
+a_b_c  =  3*c1
+q1, q2, u1, u2 = _me.dynamicsymbols('q1 q2 u1 u2')
+q1_d, q2_d, u1_d, u2_d = _me.dynamicsymbols('q1_ q2_ u1_ u2_', 1)
+x, y = _me.dynamicsymbols('x y')
+x_d, y_d = _me.dynamicsymbols('x_ y_', 1)
+x_dd, y_dd = _me.dynamicsymbols('x_ y_', 2)
+yy = _me.dynamicsymbols('yy')
+yy = x*x_d**2+1
+m = _sm.Matrix([[0]])
+m[0] = 2*x
+m = m.row_insert(m.shape[0], _sm.Matrix([[0]]))
+m[m.shape[0]-1] = 2*y
+a = 2*m[0]
+m = _sm.Matrix([1,2,3,4,5,6,7,8,9]).reshape(3, 3)
+m[0,1] = 5
+a = m[0, 1]*2
+force_ro = q1*frame_n.x
+torque_a = q2*frame_n.z
+force_ro = q1*frame_n.x + q2*frame_n.y
+f = force_ro*2