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from sympy import * | ||
import numpy as np | ||
from lib_Mathematica import frs | ||
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n,m,m1,m2,m3,m4,M,g,x,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,y,y1,y2,X,Y,a,a1,a2,a3,v,v1,v2,M1,M2,M3, V ,V1 ,V2= symbols('n m m1 m2 m3 m4 M g x x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 y y1 y2 X Y a a1 a2 a3 v v1 v2 M1 M2 M3 V V1 V2 ') | ||
w,w1,w2,aw,aw1,aw2,F,F1,F2,Rx,Ry,r,r1,r2,R,ax,ax1,ax2,ay,ay1,ay2= symbols('w w1 w2 aw aw1 aw2 F F1 F2 Rx Ry r r1 r2 R a_x ax1 ax2 a_y ay1 ay2') | ||
mu,mu1,mu2,fr,fr1,fr2,f1, f2, f3,N1,N2,N3,Nm, L,L1,L2,h,h1,h2,b,H= symbols('mu mu1 mu2 fr fr1 fr2 f1 f2 f3 N1 N2 N3 Nm L L1 L2 h h1 h2 b H') | ||
R1,R2,R3,rx,ry,fx1,fx2,fx3,fy1,fy2,fy3=symbols('R1 R2 R3 rx ry fx1 fx2 fx3 fy1 fy2 fy3') | ||
alpha,tetha,t1, t2=symbols('alpha tetha t1 t2') | ||
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at,an=symbols('a_t a_n') | ||
vx,vy,In ,Fc,ac,aw =symbols('v_x v_y I_n F_c a_c a_w') | ||
t,vxy,Po,Ti,I_n, a_c,a_t, Io=symbols('t vxy Po Ti In ac at Io') | ||
T,T1,T2,t1,t2,t3 =symbols('T T1 T2 t1 t2 t3') | ||
K,k,X1,X2,X0,d,W,P=symbols('K k X1 X2 X0 d W P') | ||
rho,z,z1,z2,A,p=symbols('rho z z1 z2 A p') | ||
xo,yo,zo,beta,xi,xf,x1,x2,y1,y2=symbols('xo yo zo beta xi xf x1 x2 y1 y2') | ||
yp,xp,pp=symbols("y' x' p'") | ||
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A,A1,A2,B,B1,B2,C,C1,C2,D,D1,D2,Q,Q1,Q2,S,S1,S2,Z,Z1,Z2=symbols('A A1 A2 B B1 B2 C C1 C2 D D1 D2 Q Q1 Q2 S S1 S2 Z Z1 Z2') | ||
# diff variables | ||
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dm,ds,dx,dy,dz,dt,dr,dh,dL,da,dA,dv,dV,dM,=symbols('dm ds dx dy dz dt dr dh dL da dA dv dV dM') | ||
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Vo,Lo,Xo,Yo,Zo=symbols('Vo Lo Xo Yo Zo') | ||
Fx1,Fy1,To1=symbols('Fx1 Fy1 To1') | ||
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# constantes | ||
A53=atan(frs(4,3)) # ang 53 = atan(4/3) | ||
A37=atan(frs(3,4)) # ang 37 = atan(3/4) | ||
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S53=frs(4,5) # ang 53 | ||
C53=frs(3,5) | ||
T53=frs(4,3) | ||
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S37=frs(3,5) # ang 37 | ||
C37=frs(4,5) | ||
T37=frs(3,4) | ||
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S45= sqrt(2)/2 # ang 45 | ||
C45=sqrt(2)/2 | ||
T45=1 | ||
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S30=frs(1,2) # ang 30 | ||
C30=sqrt(3)/2 | ||
T30=sqrt(3)/3 | ||
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S60=sqrt(3)/2 # ang 60 | ||
C60=frs(1,2) | ||
T60=sqrt(3) | ||
from IPython import display | ||
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import matplotlib.pyplot as plt | ||
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from PIL import Image # to load images | ||
from IPython.display import display # to display images | ||
dx,dy,dz,dw,du,dv=symbols( 'dx dy dz dw du dv') | ||
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def kkdis(sval): | ||
sR = sval+' = ' | ||
sV = eval(sval) | ||
display(Math(sR + latex(sV))) | ||
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from libaldo_math2 import * | ||
from libaldo_algorith import * | ||
from mathexponencial import * | ||
from mathbasic import * | ||
from sympy import * | ||
## PARTIAL FRACTION... | ||
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def primesymboldiff(var): | ||
svar=str(var) | ||
dsvar1=svar+"'" | ||
dsvar2=svar+"''" | ||
kres= dsvar1+' '+dsvar2 | ||
dsvar1=symbols(dsvar1) | ||
dsvar2=symbols(dsvar2) | ||
return dsvar1,dsvar2 | ||
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def functiondiff(QQ,var,var2): | ||
ksym=QQ.ksym | ||
f=Function(str(var2))(var) | ||
ksym2=subsubs(ksym,var2,f) | ||
kres=diff(ksym2,var) | ||
return kres | ||
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def sympydiff2prime(expr,var,var2): | ||
Y=symbols(str(var2)) | ||
p1=str(expr) | ||
svar=str(var2) | ||
dy,dy2=primesymboldiff(var2) | ||
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p2='d'+str(var2) | ||
p3=p2+'2' | ||
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F=Function(str(var2))(var) | ||
df=F.diff(var) | ||
df2=F.diff(var,var) | ||
p4=str(df) | ||
p5=str(df2) | ||
p1=p1.replace(p5,p3) | ||
p1=p1.replace(p4,p2) | ||
p1=p1.replace(str(F),svar) | ||
fres=eval(p1) | ||
fres=fres.subs(p3,dy2) | ||
fres=fres.subs(p2,dy) | ||
fres=fres.subs(F,Y) | ||
return fres | ||
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def primediff2sympy(expr,var,var2): | ||
dp2=str(var2)+"''" | ||
dp1=str(var2)+"'" | ||
yvar=str(var2) | ||
xvar=str(var) | ||
f=Function(yvar)(var) | ||
df=diff(f,var) | ||
df2=diff(f,var,var) | ||
sf=yvar+'('+xvar+')' | ||
sdf=str(df) | ||
sdf2=str(df2) | ||
sexpr=str(expr) | ||
sexpr=sexpr.replace(dp2,'D2') | ||
sexpr=sexpr.replace(dp1,'D1') | ||
sexpr=sexpr.replace(yvar,sf) | ||
sexpr=sexpr.replace('D2',sdf2) | ||
sexpr=sexpr.replace('D1',sdf) | ||
return parse_expr(sexpr) | ||
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def changedview(expr,var1,var2): | ||
sexpr=str(expr) | ||
if "'" in sexpr: | ||
return primediff2sympy(expr,var1,var2) | ||
else: | ||
return sympydiff2prime(expr,var1,var2) | ||
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