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Libaldo/lib_Variables.py

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+
+
+
+from sympy import *
+import numpy as np
+from lib_Mathematica import frs
+
+
+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')
+
+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'") 
+
+
+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
+
+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')   
+
+Vo,Lo,Xo,Yo,Zo=symbols('Vo Lo Xo Yo Zo')
+Fx1,Fy1,To1=symbols('Fx1 Fy1 To1')
+
+# constantes
+A53=atan(frs(4,3)) # ang 53 = atan(4/3)
+A37=atan(frs(3,4)) # ang 37 = atan(3/4)
+
+S53=frs(4,5) # ang 53
+C53=frs(3,5)
+T53=frs(4,3)
+
+S37=frs(3,5) # ang 37
+C37=frs(4,5)
+T37=frs(3,4)
+
+S45= sqrt(2)/2 # ang 45
+C45=sqrt(2)/2
+T45=1
+
+S30=frs(1,2) # ang 30
+C30=sqrt(3)/2
+T30=sqrt(3)/3
+
+S60=sqrt(3)/2 # ang 60
+C60=frs(1,2)   
+T60=sqrt(3) 
+from IPython import display
+
+
+import matplotlib.pyplot as plt
+
+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')
+
+def kkdis(sval):
+    sR = sval+' = '
+    sV = eval(sval)
+    display(Math(sR + latex(sV))) 
+
+

Libaldo/lib_funcdiff.py

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+
+
+from  libaldo_math2 import *
+from  libaldo_algorith import *
+from  mathexponencial  import *
+from  mathbasic import * 
+from sympy import *
+## PARTIAL FRACTION...
+
+def primesymboldiff(var):
+    svar=str(var)
+    dsvar1=svar+"'"
+    dsvar2=svar+"''"
+    kres=  dsvar1+' '+dsvar2
+    dsvar1=symbols(dsvar1)
+    dsvar2=symbols(dsvar2)
+    return dsvar1,dsvar2
+
+def functiondiff(QQ,var,var2):
+    ksym=QQ.ksym
+    f=Function(str(var2))(var)
+    ksym2=subsubs(ksym,var2,f)
+    kres=diff(ksym2,var)
+    return kres
+
+def sympydiff2prime(expr,var,var2):
+    Y=symbols(str(var2)) 
+    p1=str(expr)   
+    svar=str(var2) 
+    dy,dy2=primesymboldiff(var2)
+
+    p2='d'+str(var2)
+    p3=p2+'2'
+
+    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 
+
+
+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)
+
+
+def changedview(expr,var1,var2):
+    sexpr=str(expr)
+    if "'" in sexpr:
+         return primediff2sympy(expr,var1,var2)
+    else:
+         return sympydiff2prime(expr,var1,var2) 
+