mod

Find the modulus after division when both the dividend and divisor are integers.

Find the modulus after division for these numbers.

m = [mod(sym(27),4), mod(sym(27),-4), mod(sym(-27),4), mod(sym(-27),-4)]

m = $$\left(\begin{array}{cccc}3& -1& 1& -3\end{array}\right)$$

Find the modulus after division when the dividend is a rational number, and the divisor is an integer.

Find the modulus after division for these numbers.

m = [mod(sym(22/3),5), mod(sym(1/2),7), mod(sym(27/6),-11)]

m = 
$$\left(\begin{array}{ccc}\frac{7}{3}& \frac{1}{2}& -\frac{13}{2}\end{array}\right)$$

Find the modulus after division when the dividend is a polynomial expression, and the divisor is an integer. If the dividend is a polynomial expression, then mod returns a symbolic expression without evaluating the modulus.

Find the modulus after division by $$10$$ for the polynomial $$x^3-2x+999$$.

syms x
a = x^3 - 2*x + 999;
mUneval = mod(a,10)

mUneval = $$x^3-2\hspace{0.17em}x+999\mathrm{ mod }10$$

To evaluate the modulus for each polynomial coefficient, first extract the coefficients of each term using coeffs.

[c,t] = coeffs(a)

c = $$\left(\begin{array}{ccc}1& -2& 999\end{array}\right)$$

t = $$\left(\begin{array}{ccc}{x}^3& x& 1\end{array}\right)$$

Next, find the modulus of each coefficient in c divided by 10. Reconstruct a new polynomial using the evaluated coefficients.

cMod10 = mod(c,10);
mEval = sum(cMod10.*t)

mEval = $$x^3+8\hspace{0.17em}x+9$$

For vectors and matrices, mod finds the modulus after division element-wise. When both arguments are nonscalar, they must have the same size. If one argument is a scalar, the mod function expands the scalar input into an array of the same size as the other input.

Find the modulus after division for the elements of two matrices.

A = sym([27,28; 29,30]);
B = sym([2,3; 4,5]);
M = mod(A,B)

M = 
$$\left(\begin{array}{cc}1& 1\\ 1& 0\end{array}\right)$$

Find the modulus after division for the elements of matrix A and the value 9. Here, mod expands 9 into the 2-by-2 matrix with all elements equal to 9.

M = mod(A,9)

M = 
$$\left(\begin{array}{cc}0& 1\\ 2& 3\end{array}\right)$$

Create two periodic functions that represents sawtooth waves.

Define the sawtooth wave with period T = 2 and amplitude A = 1.5. Create a symbolic function y(x). Use mod functions to define the sawtooth wave for each period. The sawtooth wave increases linearly for a full period, and it drops back to zero at the start of another period.

T = 2;
A = 1.5;
syms y(x);
y(x) = A*mod(x,T)/T;

Plot this sawtooth wave for the interval [-6 6].

fplot(y,[-6 6])

Next, create another sawtooth wave that is symmetrical within a single period. Use piecewise to define the sawtooth wave that is increasing linearly for the first half of a period, and then decreasing linearly for the second half of a period.

y(x) = piecewise(0 < mod(x,T) <= (T/2), 2*A*mod(x,T)/T,...
                 (T/2) < mod(x,T) <= T, 2*A - 2*A*mod(x,T)/T);

Plot this sawtooth wave for the interval [-6 6].

fplot(y,[-6 6])