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CAS Book: Doing Mathematics withScientic WorkPlace (MuPAD kernel)
06-15-2018, 03:30 PM (This post was last modified: 09-24-2018 04:35 PM by compsystems.)
Post: #1
CAS Book: Doing Mathematics withScientic WorkPlace (MuPAD kernel)
free book "Doing Mathematics with Scientic WorkPlace", The MuPAD kernel (now owned by Matlab) is bundled with Scientific Notebook and Scientific Workplace Software.

[Image: 51ATKQJ50ZL._SX258_BO1,204,203,200_.jpg]

https://www.sciword.co.uk/manuals/
http://ftp.ftp.mackichan.com/download/ve...ath-55.pdf
http://ftp.ftp.mackichan.com/download/ve...ath-60.pdf

A good book with many CAS examples

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09-24-2018, 02:05 PM (This post was last modified: 09-24-2018 02:10 PM by compsystems.)
Post: #2
RE: CAS Book: Doing Mathematics withScientic WorkPlace
Hello, I am transcribing the examples of the book, they are executed both in xcas and hp-prime, except that in the hp-prime there are some instructions not yet ported.


PHP Code:
cas_setup([0,0,0,1,160,[1e-12,1e-15],12,[1,100,0,25],0,1,0,1]); // Default settings

/* I. Elementary Number Theory */
/* integers into products of powers of primes */
ifactor(12345// A prime is an integer greater than 1 whose only positive factors are itself and 1.
ifactor(-24), ifactor(24!)
/* Greatest Common Divisor  */
gcd(a,b// The greatest common divisor of two integers is the largest integer that divides both integers evenly.
gcd(351565
gcd(2^14 3^5^93^7^3), gcd(-104221)
/* Least Common Multiple */
lcm(a,b
lcm(351565
lcm(68); lcm(104221)
/* Factorials */
[a!, 0!, 3!, 7!, 10!] // Factorial is the function of a nonnegative integer n denoted by n! and defined for positive integers n as the product of all positive integers up to and including n; that is, n! = 1*2*3*4*...n. It is defined for zero by 0! = 1
/* Binomial Coefficients */
'(a + b)^n=sum((n!/(k!*(n-k)!))*(a^(n-k)*b^k),k,0,n)' //  An expression of the form a + b is called a binomial. the formula that gives the expansion of (a + b)^n for any natural number n is
binomial(a,b// binomial coefficients.   
binomial(5,2
binomial(a,5), factor(a!/(5!*(a-5)!))
/* Real Numbers */
/* Arithmetic.  The real numbers include the integers and fractions (rational numbers), as well as irrational numbers such as sqrt(2) and pi that cannot be expressed as quotients of integers. */
9.6*pi 2.7*pi // qpi(9.6*pi - 2.7*pi)
42*( 2/1/) * sqrt(2)
(
2/3) / (8/7
/* changea floating point number to a rational number. */
exact(0.125// rational
exact(4.72
exact(6.9*pi)
exact(3.1416 
/* Evaluating float at a rational number gives the floating point form of the number. */

approx(3927/12501/8// Numerical Approximations
/* Powers and Radicals Pag 34 */
[3^4, (2.5)^(4/5), 3^-40.4^32// To raise numbers to powers use ^ symbol
surd(0.008,3); surd(18.234,5); surd(24,2); surd(16/27,3); surd(16,4); surd(-8,3// Radical notation for roots
autosimplify(2):; surd(16/27,3// irrational number
autosimplify(2):; surd(16/27,3)
autosimplify(2):; surd(162*pi^6,4)
approx(3*pi*(2*pi^2)^(1/4)); approx(3*pi^(3/2)*surd(2,4))
autosimplify(0):; surd(162*pi^6,4)
autosimplify(1):; surd(162*pi^6,4)
autosimplify(2):; 1/sqrt(2// Rationalizing a Denominator
autosimplify(0):; 1/sqrt(2)
autosimplify(2):; 1/(sqrt(2)+sqrt(3))
autosimplify(1):; 1/(sqrt(2)+sqrt(3))
autosimplify(2):; (sqrt(2)+sqrt(3))/(sqrt(5)-sqrt(7))
autosimplify(0):; (sqrt(2)+sqrt(3))/(sqrt(5)-sqrt(7))
autosimplify(0):; -1/* (sqrt(2) + sqrt(3)) * (sqrt(5) + sqrt(7))
/* Functions and Relations */
abs(a// Absolute value
abs(-11.3)
max(a,b); min(a,b); // Maximum and Minimum
max12/3,-sqrt(63), 7.3 )
min12/3,-sqrt(63), 7.3 
max2765/2, -14 )
min2765/2, -14 )
floor(5.6); ceil(5.6// Greatest and Smallest Integer Functions 
floor(43/5); ceil(43/5)
floor(-11.3); ceil(-11.3)
floor(pi+e); ceil(pi+e)
evalbe^(i*pi) = -// Checking Equalities and Inequalities
evalbpi=3.14 )
evalbasin(sin(a)=a) )
asin(sin(a))
evalb( (9/8-8/9) = abs(9/8-8/9) )
evalbpi^e-e^pi abs(pi^e-e^pi) )
pi^e-e^pi abs(pi^e-e^pi)
(
9/8) < (8/9)
pi^e^pi
evalb
(sqrt(2)^2=2)
(
5^6^5) and (1=1); (5^6^5) and (1=1)
(
5^6^5) or (1=1); (5^6^5) or (1=1)
(
1) or (1=0)
e^pi pi^) and (0=0)
/* Union, Intersection, and Difference */
set[1,2,3union set[a,b,c]
[
1,2,3union ([3,5union [7])
[
sqrt(2), pi3.9runion [a,b,c]
[
1,2,3intersect [2,4,6]
[
1,2,3intersect [a,b,c]
[
a,b,cdintersect [deef]
set[]
[
1,2,3intersect []
[
1,2,3minus [2,4]
[
1,2,3minus [a,b,c]
[
a,b,c,dminus [deef]
/* Complex Numbers */
i
sqrt
(-5)
i/(1+i)
abs(i// Absolute Value
abs(1+i)
conj(a+i); conj(1+i)// Complex conjugate
re(i); im(3*i)  // Real and Imaginary Parts
6_ft 8_ft10_m 5_m  // Arithmetic Operations with Units
6_ft 8_ft
4_ft 
16_inch 
convert
(5.33333333333_ft,1_m// Converting Units
4_d 3_mn 
convert
(4.00208333333_d,1_s
10_mile/15_s
convert
((2/3)_(mile*s^-1.0),1_m/1_s
convert(7_ft,1_inch)
convert(458.4_deg,1_rad)
convert(50_mile/1_h,1_km/1_h)
convert(47_lb,1_kg)
convert(8_rad,1_deg)
1440./pi
/* Algebra, Polynomials and Rational Expressions */
(3*x^3*)+(8*x^2+7// Sum
(3*x^3*)/(8*x^2+7// Quotients of Polynomials
((1)^-1)*(1)^-// Product
((1)^-1)*(1)^-1
expand
(((1)^-1)*(1)^-1)
(
3*x^3*-)*(8*x^2+7)
(
3*x^+3*x^-4*x^5)/(8*x^+7
(
3/64)*x-( ((21/64)*- (17/2))/(8*x^2+7) ) + (3/8)*x^-1/
sum
(a[k]*x^k,k,0,5)  // summation notation
ratnormal((8x^)^-* (2x^)^-1)
x/(x^2-1) + (3*x-1)/(x^2-3*x+2)
factor(x/(x^2-1) + (3*x-1)/(x^2-3*x+2))
partfrac(36/((x-2)*((x-1)^2)*(x+1)^2)) // Partial Fractions
complex_mode(0):;partfrac((x^3+x^2+1)/(x*(x-1)*(x^2+x+1)*(x^2+1)^3))
partfracy/(((x-y)^2)*(x+1)))
partfrac(y/((x-y)^2*(x+1)),y)
partfrac(y/((x-y)^2*(x+1)),x)
cas_setup(0,0,0,1,160,[1e-12,1e-15],12,[1,100,0,25],0,1,0,1// 9-th parameter increasing power flag

x^3*53*x^5*x^4*x^13 2*x^
sort
(5*t^3*x*t^16*t^y^2*x*t^9,t)
sort(5*t^3*x*t^16*t^y^2*x*t^9)
collect(5*t^3*x*t^16*t^y^2*x*t^9,y)
5*x^5*x^10*x^10*x^5*5factor(5*x^5*x^10*x^10*x^5*5)
1/16*x^-7/5*1/6*i*56/15*i;  factor(1/16*x^-7/5*1/6*i*56/15*i)
expand((3*x+8*i)*(5*x-112)/240)
x^2*3substx^2*3x=// Substituting for a Variable
substyx=y+)
substx^2*3,x=y-); factory^2-2*y*z+2*y+z^2-2*z-3); 2*2*+ (y-z)^3
expand
2*2*+ (y-z)^)
preval(x,a,b// Evaluating at Endpoints
preval(x^2*3x=3x=5// request x=
preval(x^2*335)
preval(x^2*3ab)
purge(x):; roots(5*x^2*3); solve(5*x^2*3=0// multiplicity
list2exp([[3,9],[- 1,1]],x)
roots(x^1,x)
x^13/5*i*x^8*x^29/5*i*81/5*6*18/
solve
(x^13/5*i*x^8*x^29/5*i*81/5*6*18/=0,x)
roots(x^13/5*i*x^8*x^29/5*i*81/5*6*18/5,x)
csolve(x^13/5*i*x^8*x^29/5*i*81/5*6*18/=0,x)
5/2+(13/10*i) - 1/10*(336 850*i)
5/2+(13/10*i) + 1/10*(336 850*i)
assume(xinteger// real
roots(x^13/5*i*x^8*x^29/5*i*81/5*6*18/5,x); 
1//roots(5*x^2+x+3); // bug
purge(x):;
// roots(ax^2 + b*x + c); // bug
solve(x^3*1=0);
roots(a*x^b*c);
csolve(x^3*1=0); // exact
csolve(x^3*1.0=0); // approx
roots(x^3*1=0);
roots(x^3*x^2*x^1)
roots(x^8/3*x^5/3*2)

factor(x^8/3*x^5/3*2); expand((x-3)*(x+1)*(3*x-2)/3)
factors(x^8/3*x^5/3*2)
csolve(x^-13/5*i*x^8*x^29/5*i*81/5*6*-18/5=0)

factor(x^-13/5*i*x^8*x^29/5*i*81/5*6*-18/5)
/* Equations with One Variable */
solve(5*x^3*1)
expand(list[(-(sqrt(29))-3)/10,(sqrt(29)-3)/10])
solve(abs(3*2) =  5)

purge(x)
solve(1/1/1, [x,y],'='// no coloca restricciones
solve(1/1/1x'=')
solve(1/1/1y'=')
solve(1/1/1/1z'=')
solve([x^y^5x^y^1],[x,y],'=')
solve([x^y^5x^y^1],[x,y])
autosimplify(0):;list2exp([[sqrt(3),sqrt(2)],[-(sqrt(3)),sqrt(2)],[sqrt(3),-(sqrt(2))],[-(sqrt(3)),-(sqrt(2))]],[x,y]);
list2exp(solve([x^y^5x^y^1],[x,y]),[x,y])

/* Inequalities */
autosimplify(0):;solve(16 7*>= 10*4y)
solve(x^x^x)
solve(x^2*0x)
solve(abs(2*3) <= 1)
solve( (7-2*x)/(x-2)>=0,x)
a<x<b; ((x>a) and (x<b))
a<x<=b; ((x>a) and (x<=b))
a<=x<=b; ((x>=a) and (x<=b))
/* Defining Functions of One Variable // p 69 */
f(x) := a*x^b*c;
[
f(t), f(-6), f(17)]
f(x) := 5*3;
solve(f(y)=0)
seq(x^3*5,x,[0,1,2,3,4]); // To find the value of the expression x^2 + 3x + 5 at x = 0, 1, 2, 3, 4
seq(x=y+1,y,0,4)
subst(x^3*5,[x=1,x=2,x=3,x=4,x=5])
/* Definning Functions of Several Variables */
f(xyz) := a*y^2*z
g
(xy) := 2*sin(3*x*y)
f(123
g(1,2)
/* Piecewise-Defined Functions */
f(x):= piecewise(x<0,x+2,0<=x<=1,2x>12/x)
[
f(-14), f(1/2), f(21)]
h(x):= (1)/(1)
purge(f), purge(h)//Removing Definitions 

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