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C++ API

Function File: [y alpha] = multinom (x, n)

Function File: [y alpha] = multinom (x, n,sort)

Returns the terms (monomials) of the multinomial expansion of degree n. 

          (x1 + x2 + ... + xm)^n

x is a nT-by-m matrix where each column represents a different variable, the output y has the same format. The order of the terms is inherited from multinom_exp and can be controlled through the optional argument sort and is passed to the function sort. The exponents are returned in alpha.

See also: multinom_exp multinom_coeff sort

Demonstration 1

The following code

 n = 3;
 t = linspace(-1,1,10).';
 x = [t-1/2, t];
 y = multinom(x,n,'descend');
 y_shouldbe = [x(:,1).^3 x(:,2).^3 x(:,1).^2.*x(:,2) x(:,1).*x(:,2).^2 ];
 plot(t,y_shouldbe); hold on; plot(t,y,'s'); hold off;
 legend('x_1^3','x_2^3','x_1^2x_2','x_1x_2^2','location','southoutside',...
 'orientation','horizontal');
 title('Terms of the expansion of (x_1 + x_2)^3 (colors should match)');

Produces the following figure

Figure 1

Package: specfun