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The Maxima on-line user's manual

Algebra Calculator

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Radcan Calculator

Radcan

Function: radcan (<expr>) Simplifies <expr>, which can contain logs, exponentials, and radicals, by converting it into a form which is canonical over a large class of expressions and a given ordering of variables; that is, all functionally equivalent forms are mapped into a unique form. For a somewhat larger class of expressions, radcan produces a regular form. Two equivalent expressions in this class do not necessarily have the same appearance, but their difference can be simplified by radcan to zero.

f(x):=16*(1-x^5)/(1-x);
f(0.5);
gp(x):=(sqrt(f(x))+sum(x^k,k,2,28))/2;
gm(x):=(sqrt(f(x))-sum(x^k,k,2,28))/2;
float(subst(0.5,x,gp(x)*gm(x)));
tp(x):=taylor(gp(x),x,0,4);
float(tp(x));
tm(x):=taylor(gm(x),x,0,4);
float(tm(x));
float(subst(0.5,x,tp(x)));
float(subst(0.5,x,tm(x)));
h(x):=float(tp(x))^(1/3)-float(tm(x))^(1/3);
radcan(expand(float(ratsimp(h(x)))));
float(subst(0.5,x,h(x))/sqrt(3));

For some expressions radcan is quite time consuming. This is the cost of exploring certain relationships among the components of the expression for simplifications based on factoring and partial-fraction expansions of exponents.

Examples:

          (%i1) radcan((log(x+x^2)-log(x))^a/log(1+x)^(a/2));
                                                     a/2
          (%o1)                            log(x + 1)

          (%i2) radcan((log(1+2*a^x+a^(2*x))/log(1+a^x)));
          (%o2)                                  2

          (%i3) radcan((%e^x-1)/(1+%e^(x/2)));
                                               x/2
          (%o3)                              %e    - 1

There are also some inexact matches for radcan. Try ?? radcan to see them.

(%o1)                                true
(%i2) 

Radcan Example

Related Examples

radcan

v:(a^5*b)^(1/3);

v1:(a*b^(-3))^(1/2);

v2:radcan(v/v1);

Calculate

radcan

ta: radcan(log2(64));

Calculate

radcan-sqrt

f:a^5*b;

f1:f^(1/3);

f2:radcan(f1);

Calculate

radcan-sqrt

radcan((2+sqrt(5))/(3...

Calculate

radcan-sin

radcan(sin(ln(x^2)));

Calculate

radcan-sin-subst-trigexpand

f:sin(a+b);

g:trigexpand(f);

h:subst([a=%pi/12*3,b...

Calculate

radcan

v:(a^5*b)^(1/3);

v1:(a*b^(-3))^(1/2);

v2:radcan(v/v1);

Calculate

radcan-rhs-solve-subst

f:2*x^2-4*x-3;

g:solve(y=f,x);

g:rhs(g[2]);

Calculate

radcan-sqrt

radcan(sqrt(x^2+y^2));

Calculate

radcan-sqrt

AB: 5;

BC: sqrt(106);

CA: sqrt(41);

Calculate