Use of Scilab in secondary school mathematics

[Number]

Define numbers
a=1
b=2;c=3;d=4;e=5;

Simple calculation
a+b*c-d/e

Elementary functions
log(100)
sin(%pi/6)
4^2
sqrt(4)
27^(1/3)
3D-4

[Polynomial]

Define a polynomial
x+1

(1) Direct input
x=poly(0,'x')
p=x+1
q=2+3*x-4*x^2
x=poly(2,・s・);2*x+1

(2) By coefficients
f=poly([1,3,5,-7],'x','coeff')

(3) By roots
g=poly([1,2,3],'x')

Simple computations
- Value of polynomial
horner(g,4)

- Addition
- Subtraction
- Multiplication
f+g
f-2*g
f*g
x=poly(0,・x・);(1+x)^5

Division
f/g

- Quotient
- Reminder
[r,q]=pdiv(f,g)
checking: q*g+r

Solving polynomial equations
roots(x^2-5*x-6)

p=x^3-4*x^2+5*x-7;
roots(p)

Factorization
polfact(2*x^2-50)

G.C.D. and Euclidean Algorithm
f=4*x^4-2*x^3-16*x^2+5*x+9;
g=2*x^3-x^2-5*x+4;
gcd([f,g])

Find polynomials u, v such that u*f + v*g = d
d=gcd([f,g]);
[w,a]=diophant([f,g],d)
checking: w(1,1)*f+w(2,1)*g

Find g.c.d. (H.C.F.) among integers
v=int32([12,15]);
gcd(v)

Find l.c.m. (L.C.M.) among integers
lcm(v)

Partial fraction
s=poly(0,・s・);
pfss((23*s-11*s^2)/(-2*s^3+s^2+18*s-9))

[Matrix]

Define a matrix
M=[1 2;3 4]
N=[1,2,3;4,5,6]
C=[];C(3,2)=1
D=diag([1,2,3])

Simple computations
M=[1 2;3 4];N=[5 6;7 8];
M+N
M*N
M^3

Matrix of polynomials
M=[x,2-x;3*x+1,x-3]
M^2

Self operations
M=[1 2;3 4];
M'
det(M)
inv(M)
checking: inv(M)*M
spec(M)

Calculus
Differentiation
x=poly(0,'x');
derivat(x^2/(x-1))

Integration
- Define a function first
function y=f(x),y=sin(x),endfunction
intg(0,%pi,f)

Plotting
2D
t=linspace(0,2*%pi);y=sin(t);plot(y)

3D
clear
A=[1 2 2 1 0;2 3 4 6 3;3 2 1 2 2;1 1 2 3 2];
t1=1:4;
t2=1:5;
plot3d1(t1,t2,A);