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Mathematics Example

In addition to being a powerful computation engine for higher-level knowledge, SubjectMate|solver can also solve math problems, such as elementary math, algebra, geometry, plotting graph, calculus and analysis, differential equation, statistic, and mathematical functions.

Arithmetic

Execute all arithmetic operations.

Basic arithmetic operations:

Square roots operations:

Place Value

Place values for decimal numbers.

Show place value:

place values of 8965

Find place value:

value of the digit 7 in 257394

Fraction

Perform fraction.

Fraction addition:

1/3 + 7/10 + 2/4

Fraction Multiply:

Fraction arithmetic operations:

1/6 * (5 - 1/3)

Percentages

Perform percentage problems.

Convert from fraction to percentage:

convert 2/7 to percent

Calculate a discount price:

35% off of $45.87

Solve percentage of a quantity:

45% of 9.5 miles

Number Type Arithmetic

Execution on signs, categories and numbers type.

Determine parity:

even number ^ positive integer

Determine sign:

negative integer * negative integer

Determine number type:

square root of integer

Mathematical Word Problems

Examine the related facts for a math word problem.

Solve a word problem:

Jimmy has 7 cats and 3 dogs. Julie has 5 cats and 6 dogs. How many dogs are there in all?

Rhonda has 13 marbles more than Douglas. Douglas has 8 marbles more than Bertha. Rhonda has twice as many marbles as Bertha has. How many marbles does Douglas have?

Equation Execution

Execute equations in both symbolically and numerically.

A specified equations:

solve x^3 - 4x^2 + 6x - 24 = 0 over the reals

A polynomial equation:

solve x^2 + 4x + 6 = 0

A trigonometric equation:

sin x + cos x = 1

Systems of congruences:

solve 2x = 10 (mod 12), 3x = 9 (mod 12)

Numerical Root

Numerical approximation methods.

Find equation root using Newton's method:

using Newton's method solve x cos x = 0

Find equation root using the secant method:

solve x^2 + 4x + 6 = 0

Compute the n^th root of a number using the bisection method:

find root of 2 with bisection method

Specify a starting point:

newton-raphson x^3 - 15x + 10 start at 2.25

Matrices

Matrices properties and computations.

Simple arithmetic execution on matrices:

{{0,-1},{1,0}}.{{1,2},{3,4}}+{{2,-1},{-1,2}}

Find the eigenvalue of a matrix:

eigenvalues {{4, 1}, {2, -1}}

Find the trace of a matrix:

tr {{9, -6, 7}, {-9, 4, 0}, {-8, -6, 4}}

Find the LU decomposition of a square matrix:

LU decomposition of {{7, 3, -11}, {-6, 7, 10}, {-11, 2, -2}}

Simplification

Simplify algebraic expressions and functions.

Simplify the algebraic expression:

simplify x^5-20x^4+163x^3-676x^2+1424x-1209

Simplify boolean algebraic expression

Simplify A And B Or A And Not B

Complete a square:

complete the square x^2+10x+28

Find a partial fraction decomposition:

partial fractions (x^2-4)/(x^4-x)

Finite Groups & Finite Fields

Find information about a finite group or discover properties of fields containing a finite number of elements.

Get information about a finite group:

symmetric group S3

Find properties of a finite field:

Do algebra with permutations:

perm (1 2 3 4)^3(1 2 3)^-1

Compute a specific property:

number of primitive polynomials of GF(3125)

Quaternions

Execute and perform operations on quaternion expressions.

Compare quaternions:

Quaternion(+11/11,-2,3,2), Quaternion(11,-2,0,-2)

Do calculations with quaternions:

quaternion -Sin[Pi]+3i+4j+3k multiplied by -1j+3.9i+4-3k

inverse of quaternion 1+0i+0j+2k ** (-1i+3+4j+3k)

Visualize a quaternion:

draw 1+0i+5j+2k as a rotation operator