# Please do not post homework
# Matthew Esaia, January 26, Assignment 1

# 1.2 Basic syntax

print(`Section 1.2`);
105/25-1/5;
% + 1/5;

# 2.1 Exact arithmetic and basic functions

print(`Section 2.1`);
2/3  + 3/5;
#12^20;

# 2.2 Floating-point arithmetic
 
print(`Section 2.2`);
tan(Pi/5);
evalf(%);
E := exp(1): evalf(E, 20);
Digits := 30;
evalf(E);

Digits := 10;
evalf(sin(Pi/6));
convert(%, rational);

# 3.1 Polynomials and rational functions

print(`Section 3.1.1`);
p := x^2 + 5*x + 6;
factor(p);

print(`Section 3.1.2`);
p := (x + 2) * (x + 3);
expand(%);

print(`Section 3.1.3`);
(x + y + 1) * (x - y + 1) * (x - y - 1);
p := expand(%);
collect(p, x);

print(`Section 3.1.4`);
3 * 4^(1/2) + 5;
simplify(%);

x^2;
y := %^(1/2);
assume(x > 0);
simplify(y);

x := 'x'; # Removes the assumption that x > 0

print(`Section 3.1.5`);
y := x^3 + 3 * x^2 + 3 * x + 1;
simplify(y^(1/3));
radsimp(y^(1/3));

readlib(rationalize): # Some packages use readlib instead of with
1/(1+sqrt(2));
rationalize(%);

print(`Section 3.1.6`);
a := 2 * x^3 + x^2 + 12;
b := x^2 - 4;
q := quo(a, b, x);
r := rem(a, b, x);
expand(a - (b * q + r));

print(`Section 3.1.7`);
x := 'x':
y := 'y':
p := (x + y + 1) * (x - y + 1) * (x - y - 1):
q := expand(%):
coeff(q, x, 2);
coeff(p, x, 2);
degree(q, x);

print(`Section 3.1.8`);
p := (x + y + z) * (x - y + z) * (x - y - z);
subs(x = 1, y = 2, p);

# 3.2 Equations
print(`Section 3.2.1`);
eqn := x^2 - x = 1;
R := solve(eqn, x);
simplify(R[1]*R[2]);

print(`Section 3.2.2`);
a := 'a':
eqn1 := x^3 + a*x = 14:
eqn2 := a^2 - x = 7:
solve({eqn1, eqn2}, {x, a});
#%[1];
#assign(%);
#a; x;

# 3.3 Fun with integers
print(`Section 3.3.1`);
ifactor(2^(2^5)+ 1); # Prime factorization

print(`Section 3.3.4`);
ithprime(100);
isprime(2^101 - 1);

# isolve -> gives you an integer solution