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complex-domain-solve

eq1: z12=R1+%i*(w*L1-...

eq2: 1/z23=(1/(R2-(%i...

eq3: z13=z12+z23;

Calculate

complex-declare-domain-factor-rectform-solve

domain:complex;

declare([a1,b1,a2,b2,...

eq1:a1*zA1+b1=a2*zA2+b2;

Calculate

complex-define-determinant-domain-hessian

domain:complex;

define(F(x,y,z),(z+y+...

define(H(x,y,z),deter...

Calculate

complex-diff-domain-sqrt

domain:complex;

F(x,y,z):=(z+(3/2)*y+...

YY(x,y,z):=diff(diff(...

Calculate

complex-define-diff-domain

domain:complex;

define(F(x,y,z),(z+y-...

diff(diff(diff(F(x,y,...

Calculate

complex-declare-partfrac

declare(x, complex);

partfrac((x0**2*(z*x*...

Calculate

complex-domain-imagpart-makelist-plot2d-realpart
plot2d([[discrete,ReList,ImList],[discrete, ReList,ImList]],[x,-15,15],[y,-15,15],[style, points, lines]);

domain:complex;

ImList:makelist(imagp...

ReList:makelist(realp...

Calculate

complex-display2d-domain-false-ratprint-solve

domain:complex;

display2d:false;

ratprint:false;

Calculate

complex-cos-domain-ev-sin-solve-true

domain:complex;

rce1:sin(x)=cos(x)-1;

solve(rce1,x);

Calculate

complex-declare-define-determinant-domain-matrix-sqrt

domain:complex;

declare([a,b,c,d,e,f,...

declare([S,J],real);

Calculate

complex

Run Example
(%i1)domain:complex;
(%o1)                               complex
(%i2) define(F(x,y,z),(z+y-x)*(z-y-x)*(z+(%i)*y+x)*(z-(%i)*y+x));
(%o2) F(x, y, z) := (z - y - x) (z + y - x) (z - %i y + x) (z + %i y + x)
(%i3) define(ZZ(x,y,z),diff(diff(F(x,y,z),z),z));
(%o3) ZZ(x, y, z) := 2 (z - %i y + x) (z + %i y + x)
 + 2 (z + y - x) (z + %i y + x) + 2 (z - y - x) (z + %i y + x)
 + 2 (z + y - x) (z - %i y + x) + 2 (z - y - x) (z - %i y + x)
 + 2 (z - y - x) (z + y - x)
(%i4) define(YY(x,y,z),diff(diff(F(x,y,z),y),y));
(%o4) YY(x, y, z) := - 2 (z - %i y + x) (z + %i y + x)
 + 2 %i (z + y - x) (z + %i y + x) - 2 %i (z - y - x) (z + %i y + x)
 - 2 %i (z + y - x) (z - %i y + x) + 2 %i (z - y - x) (z - %i y + x)
 + 2 (z - y - x) (z + y - x)
(%i5) define(YZ(x,y,z),diff(diff(F(x,y,z),y),z));
(%o5) YZ(x, y, z) := - %i (z + y - x) (z + %i y + x)
 - (z + y - x) (z + %i y + x) - %i (z - y - x) (z + %i y + x)
 + (z - y - x) (z + %i y + x) + %i (z + y - x) (z - %i y + x)
 - (z + y - x) (z - %i y + x) + %i (z - y - x) (z - %i y + x)
 + (z - y - x) (z - %i y + x)
(%i6) diff(ZZ(x,y,z),x);
(%o6) - 2 (z + %i y + x) - 2 (z - %i y + x) + 2 (z + y - x) + 2 (z - y - x)
(%i7) 
Run Example
domain:complex;
(%o1)                               complex
(%i2) declare([a1,b1,a2,b2,zA1,zB1,zA2,zB2],complex);
(%o2)                                done
(%i3) eq1:a1*zA1+b1=a2*zA2+b2;
(%o3)                      a1 zA1 + b1 = a2 zA2 + b2
(%i4) eq2:a1*zB1+b1=a2*zB2+b2;
(%o4)                      a1 zB1 + b1 = a2 zB2 + b2
(%i5) sol:solve([eq1,eq2], [a2, b2]);
             a1 zA1 - a1 zB1       - a1 zA1 zB2 - b1 zB2 + zA2 (a1 zB1 + b1)
(%o5) [[a2 = ---------------, b2 = -----------------------------------------]]
                zA2 - zB2                          zA2 - zB2
(%i6) solf:factorsum(factor(sol));
             a1 (zB1 - zA1)       a1 zA1 zB2 + b1 zB2 - a1 zA2 zB1 - b1 zA2
(%o6) [[a2 = --------------, b2 = -----------------------------------------]]
               zB2 - zA2                          zB2 - zA2
(%i7) 
Run Example
domain:complex;
(%o1)                               complex
(%i2) declare([a1,b1,a2,b2,zA1,zB1,zA2,zB2],complex);
(%o2)                                done
(%i3) eq1:a1*zA1+b1=a2*zA2+b2;
(%o3)                      a1 zA1 + b1 = a2 zA2 + b2
(%i4) eq2:a1*zB1+b1=a2*zB2+b2;
(%o4)                      a1 zB1 + b1 = a2 zB2 + b2
(%i5) sol:solve([eq1,eq2], [a2, b2]);
             a1 zA1 - a1 zB1       - a1 zA1 zB2 - b1 zB2 + zA2 (a1 zB1 + b1)
(%o5) [[a2 = ---------------, b2 = -----------------------------------------]]
                zA2 - zB2                          zA2 - zB2
(%i6) solf:factor(sol);
             a1 (zB1 - zA1)       a1 zA1 zB2 + b1 zB2 - a1 zA2 zB1 - b1 zA2
(%o6) [[a2 = --------------, b2 = -----------------------------------------]]
               zB2 - zA2                          zB2 - zA2
(%i7) 
[complex,conjugate,declare,matrix,transpose] [complex,conjugate,declare,ratsimp,realpart] [complex,conjugate,declare,ratsimp] [complex,conjugate,declare] [complex,cos,domain,ev,sin,solve,true] [complex,declare,define,determinant,domain,factor,matrix,sqrt] [complex,declare,define,determinant,domain,matrix,sqrt] [complex,declare,define,determinant,domain,matrix] [complex,declare,domain,factor,rectform,solve] [complex,declare,domain,factorsum,solve] [complex,declare,domain,rectform,solve] [complex,declare,factor,imagpart,realpart,solve] [complex,declare,imagpart,ratsimp,realpart] [complex,declare,imagpart,realpart,solve] [complex,declare,imagpart,realpart] [complex,declare,solve] [complex,define,determinant,diff,domain,factor,hessian] [complex,define,determinant,domain,factor,hessian] [complex,define,determinant,domain,hessian] [complex,define,diff,domain,solve,sqrt] [complex,define,diff,domain] [complex,determinant,diff,domain,factor,hessian,sqrt] [complex,determinant,domain,factor,hessian,sqrt] [complex,diff,display2d,domain,expand,false,float,ratprint,rhs,solve] [complex,diff,display2d,domain,expand,false,ratprint,solve] [complex,diff,display2d,domain,false,fullratsimp,ratprint,rhs,solve,subst] [complex,diff,display2d,domain,false,ratprint,solve] [complex,diff,domain,sqrt] [complex,display2d,domain,false,ratprint,solve] [complex,domain,ev,solve,true] [complex,domain,factor,hessian,sqrt] [complex,domain,imagpart,makelist,plot2d,realpart] [complex,domain,imagpart] [complex,domain,log,solve] [complex,domain,ratexpand,solve] [complex,domain,solve] [complex,domain] [complex,residue,sqrt] [complex,solve] [complex]

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