randVar()
[ BLUE, ORANGE, GREEN ]
4
tabulate( function() {
return randRangeUniqueNonZero( 0, MAX_DEGREE, randRange(1, 3) ).sort().reverse();
}, 2 )
tabulate( function(n) {
var coefs = [];
for ( var i = 0; i <= MAX_DEGREE; i++ ) {
var value = 0;
for ( var j = 0; j < NON_ZERO_INDICES[ n ].length; j++ ) {
if ( i === NON_ZERO_INDICES[ n ][ j ] ) {
value = randRangeNonZero( -7, 7 );
break;
}
}
coefs[ i ] = value;
}
return new Polynomial( 0, MAX_DEGREE, coefs, X )
}, 2 )
function() {
var likeTerms = [];
var counter = 0;
var areLikeTerms = false;
for ( var i = POL_1.minDegree; i <= POL_1.maxDegree; i++ ) {
if ( POL_1.coefs[ i ] === 0 ) {
continue;
}
for ( var j = POL_2.minDegree; j <= POL_2.maxDegree; j++ ) {
if ( POL_2.coefs[ j ] === 0 ) {
continue;
}
if ( likeTerms[ i + j ] === undefined ) {
likeTerms[ i + j ] = "";
} else if ( likeTerms[ i + j ] === "" ) {
likeTerms[ i + j ] = COLORS[ counter++ ];
areLikeTerms = true;
}
}
}
return areLikeTerms ? likeTerms : false;
}()
POL_1.multiply( POL_2 )
tabulate( function(n) {
var counter = 0;
var coefs = [];
for ( var i = 0; i < SOLUTION.coefs.length; i++ )
{
if ( SOLUTION.coefs[ i ] === 0 ) {
continue;
}
coefs[ i ] = SOLUTION.coefs[ i ] * ( n + counter++ % 2 === 0 ? 1 : -1 );
}
return new Polynomial( SOLUTION.minDegree, SOLUTION.maxDegree, coefs, SOLUTION.variable );
}, 2 )
Simplify the expression.
(POL)
SOLUTION
SOLUTION.multiply( -1 )FAKE_SOLUTION_1FAKE_SOLUTION_2
First use the distributive property.
( POL_1.coefs[ index1 ] < 0 ) ? "-" : ( n1 === 0 && n2 === 0 ) ? "" : "+"abs( POL_1.coefs[ index1 ] ) === 1 ? "" : abs( POL_1.coefs[ index1 ] )X^index1(( POL_2.coefs[ index2 ] === 1 ) ? "" : ( POL_2.coefs[ index2 ] === -1 ) ? "-" : POL_2.coefs[ index2 ]X^index2)
Simplify.
( POL_1.coefs[ index1 ] * POL_2.coefs[ index2 ] < 0 ) ? "-" : ( n1 === 0 && n2 === 0 ) ? "" : "+"abs( POL_1.coefs[ index1 ] * POL_2.coefs[ index2 ] )X^{index1 + index2}
Identify like terms.
\color{LIKE_TERMS[ index1 + index2 ]}{( POL_1.coefs[ index1 ] * POL_2.coefs[ index2 ] < 0 ) ? "-" : ( n1 === 0 && n2 === 0 ) ? "" : "+"abs( POL_1.coefs[ index1 ] * POL_2.coefs[ index2 ] )X^{index1 + index2}}
Add the coefficients.
\color{LIKE_TERMS[ SOLUTION.getCoefAndDegreeForTerm( n ).degree ]}{( SOLUTION.getCoefAndDegreeForTerm( n ).coef < 0 || n === 0 ) ? "" : "+"expr( SOLUTION.expr()[ n + 1 ] )}
You're done!