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at-cos-diff-find_root-linsolve-quad_qags-sin-subst

f: a0 + a1*s^2 + a2*s...

cond1: at(f,s=1)=0;

cond2: at(diff(f,s),s...

Calculate

at-eigenvalues-invert-jacobian

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

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

C: invert (B);

Calculate

at-rectform

at ((c*(x+%i*y)+d)^2 ...

at ((c*(x+%i*y)+d)^2 ...

Calculate

at-rat

rat(5*x^2+14*x+1, x);

Calculate

at-diff-linsolve-quad_qags-subst

f:a0+a1*s^2+a2*s^4;

cond1:at(f,s=1)=0;

cond2:at(diff(f,s),s=...

Calculate

at-rat

rat(+ 0.76895553987651);

Calculate

at-first-solve

a : 0;

b : 1;

x_1 : 0;

Calculate

at-block-diff-linsolve-plot2d-subst
plot2d(sys1(0.2),[s,0,1]);

sys1(sl1):= block(f: ...

plot2d(sys1(0.2),[s,0...

Calculate

at-float-solve

z: V1*p1/T1 = V2*p2/T2;

isop: z, p1=1, p2=1;

isoV: z, V1=1, V2=1;

Calculate

at-rat-sin

rat(((d*t)/(1+t^2))/1...

Calculate

at

Run Example
(%i1)rat(0.1234);

rat: replaced 0.1234 by 617/5000 = 0.1234
                                     617
(%o1)/R/                             ----
                                     5000
(%i2) rat(0.12345);

rat: replaced 0.12345 by 2469/20000 = 0.12345
                                     2469
(%o2)/R/                             -----
                                     20000
(%i3) rat(0.12345);

rat: replaced 0.12345 by 2469/20000 = 0.12345
                                     2469
(%o3)/R/                             -----
                                     20000
(%i4) mod(12345, 1000)/100000, numer;
(%o4)                               0.00345
(%i5) lastdigits(fnum, lastn):=block([m:10*fnum, ans, n:lastn], /* it doesn't help when lastn is bigger than the total digits in fnum it returns the whole digits in fnum anyway without erroring! and fnum=%pi stuff works only upto 8 digits cause num(rat(fnum)) has somuch only! */ratprint:false, k:rat(fnum), ans:mod(m, (10^-n))/(mod(m, 10)*denom(k)), return(float(ans)));
(%o5) lastdigits(fnum, lastn) := block([m : 10 fnum, ans, n : lastn], 
                                                   - n
                                          mod(m, 10   )
ratprint : false, k : rat(fnum), ans : -------------------, return(float(ans)))
                                       mod(m, 10) denom(k)
(%i6) lastdigits(0.12345, 3);
(%o6)                        2.0251113811259619E-8
(%i7) 
Run Example
f:5*4.57+3;
(%o1)                                25.85
(%i2) at(f,x=4,57);
(%o2)                                25.85
(%i3) df:diff(f,x);
(%o3)                                  0
(%i4) at(df,x=4.57);
(%o4)                                  0
(%i5) plot2d(df,[x,0,1]);
plotplot2d(df,[x,0,1]);
Run Example
rat(+ 0.76895553987651);

rat: replaced 0.76895553987651 by 4513/5869 = 0.76895552905095
                                     4513
(%o1)/R/                             ----
                                     5869
(%i2) 

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