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The Maxima on-line user's manual

Algebra Calculator

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At Calculator

At

Function: at (<expr>, [<eqn_1>, ..., <eqn_n>])

rat((x^4-x^3-11*x^2+9*x+18)/(x^4-3*x^3-7*x^2+27*x-18))/((x^3-9*x^2+26*x-24)/(x^3-8*x^2+19*x-12));
rat((2-x)/(x+1))*(3*x^4-24*x^3-3*x^2+204*x-252)/(220*x-70*x^2-168-15*x^3+10*x^4-x^5);
rat((x^3+2*x^2+4*x+8)/(x^5+5*x^4-16*x-80))*(2*x^4+10*x^3-16*x-80)/(x^2+2*x+4);
rat((2*x^4+10*x^3-2*x-10)/(x^2+x+1))*(x^3+x^2+x+1)/(x^5+5*x^4-x-5);
rat((4*x^4+x^5-81*x-324)/(3*x^4+10*x^3-81*x-270))*(3*x^3+19*x^2+57*x+90)/(x^4+7*x^3+21*x^2+63*x+108);
rat((4*x^5+40*x^4+100*x^3-80*x^2-320*x+256)/(x^4+x^3-9*x^2+11*x-4))*(3*x^3-3*x^2)/(x^2+8*x+16);

Function: at (<expr>, <eqn>) Evaluates the expression <expr> with the variables assuming the values as specified for them in the list of equations [<eqn_1>, ..., <eqn_n>] or the single equation <eqn>.

If a subexpression depends on any of the variables for which a value is specified but there is no atvalue specified and it cant be otherwise evaluated, then a noun form of the at is returned which displays in a two-dimensional form.

at carries out multiple substitutions in series, not parallel.

See also atvalue. For other functions which carry out substitutions, see also subst and ev.

Examples:

          (%i1) atvalue (f(x,y), [x = 0, y = 1], a^2);
                                          2
          (%o1)                          a
          (%i2) atvalue (diff (f(x,y), x), x = 0, 1 + y);
          (%o2)                        @2 + 1
          (%i3) printprops (all, atvalue);
                                          !
                            d             !
                           --- (f(@1, @2))!       = @2 + 1
                           d@1            !
                                          !@1 = 0

2 f(0, 1) = a

          (%o3)                         done
          (%i4) diff (4*f(x, y)^2 - u(x, y)^2, x);
                            d                          d
          (%o4)  8 f(x, y) (-- (f(x, y))) - 2 u(x, y) (-- (u(x, y)))
                            dx                         dx
          (%i5) at (%, [x = 0, y = 1]);
                                                   !
                        2              d           !
          (%o5)     16 a  - 2 u(0, 1) (-- (u(x, y))!            )
                                       dx          !
                                                   !x = 0, y = 1

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

(%o1)                                true
(%i2) 

At Example

Related Examples

at-cos-phi-plot3d-sin-sqrt
plot3d(at(f,r=1/rI),[rI,1/10,4],[phi,-%pi,%pi],[grid,99,30]);

f:2*r*sin(%pi/r)/sqrt...

plot3d(at(f,r=1/rI),[...

Calculate

at-diff-plot2d-sin
plot2d(df,[x,0,1]);

f:sin(x)+4.28^2;

at(f,x=4,28);

df:diff(f,x);

Calculate

at-factor-rat

rat((x^4-x^3-11*x^2+9...

rat((2-x)/(x+1))*(3*x...

rat((x^3+2*x^2+4*x+8)...

Calculate

at-rat

rat(0.81649649 - 0.16...

Calculate

at-eigenvalues-invert-jacobian

A: jacobian ([a*If*Sh...

B: jacobian ([1/r*Ih,...

C: invert (B);

Calculate

at-block-denom-float-mod-numer-rat-ratprint

rat(0.1234);

rat(0.12345);

rat(0.12345);

Calculate

at-rat-sqrt

rat(1/sqrt(2)*x^2+1);

Calculate

at-eigenvalues-invert-jacobian

A: jacobian ([a*If*Sh...

B: jacobian ([1/r*Ih,...

C: invert (B);

Calculate

at-diff-ev-exp

g(x) := x + exp(-alph...

k1 : 8.0000e+03;

k2 : 1.0000e+00;

Calculate

at

eq1:x+y+t;

eq2:x+y-z+t;

eq3:x-y+z+t;

Calculate