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The cube on the sin function is preserved.
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| (2) |
Inputting a factorable polynomial returns a factorable polynomial..
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A polynomial without integer roots returns a polynomial with random coefficients
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Factorable numerators and denominators remain factorable and if a factor is shared between the numerator and denominator then the resultant rational function will share a factor between numerator and denominator.
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| (9) |
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| (12) |
Singular matrices return singular matrices.
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| (15) |
Diagonal matrices return diagonal matrices.
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Upper triangular matrices return upper triangular matrices.
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Lower triangular matrices return lower triangular matrices.
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| (21) |
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Symmetric matrices return symmetric matrices.
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Hermitian matrices return hermitian matrices.
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| (25) |
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| (26) |
Skew-symmetric matrices return skew-symmetric matrices.
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| (27) |
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If the matrix doesn't fall into one of the above categories GenerateSimilar is mapped to every element in the matrix
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| (29) |
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| (30) |
Integration technique: u substitution.
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| (31) |
Integration technique: partial fractions.
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| (32) |
Integration technique: trig substitution.
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| (33) |
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| (34) |
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| (35) |
Integration technique: integration by parts.
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| (36) |
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| (37) |
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| (38) |
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| (39) |
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| (40) |
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| (41) |
Integration resulting in an erf function will give back integration resulting in an erf function.
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| (42) |
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| (43) |
| (44) |
Integration resulting in an Si function will give back integration resulting in an Si function.
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| (45) |
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| (46) |
| (47) |
Integration that results in an arctan function will give back integration resulting in an arctan function.
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| (48) |
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| (49) |
| (50) |
A double integral will produce a double integral;
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| (51) |
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| (52) |
A polynomial equation will produce a polynomial equation. If the input equation has integer roots the output equation will have integer roots.
| (53) |
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| (55) |
Radical equations with rational solutions will produce radical equations with rational solutions or no solutions.
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| (57) |
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| (59) |
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| (61) |
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| (63) |
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| (65) |
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| (67) |
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| (71) |
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| (75) |
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| (79) |
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| (81) |
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| (83) |
Trig equations in forms that can be solved without a calculator produce trig equations that can be solved without a calculator.
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| (85) |
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| (87) |
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| (89) |
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| (91) |
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| (93) |
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| (95) |
Logarithmic equations that are easily solvable without a calculator return logarithmic equations that can be easily solved without a calculator.
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| (97) |
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| (99) |
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| (101) |
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| (103) |
Exponential equations that can be easily solved without a calculator return exponential equations that can be easily solved without a calculator.
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| (105) |
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| (107) |
Complex polynomial equations with roots that have integer real and imaginary parts produce complex polynomial equations with integer real and imaginary roots.
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| (109) |
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| (111) |
Absolute value equations produce absolute value equations.
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| (113) |
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| (115) |
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| (117) |
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| (119) |
Equations of circles return equations of circles.
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| (121) |
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| (122) |
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Equations of ellipses return equations of ellipses.
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| (123) |
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| (124) |
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Equations of hyperbolas return equations of hyperbolas.
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| (125) |
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| (126) |
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Probability of measuring less than a certain amount of successes from a binomial distribution.
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| (127) |
Probability of measuring more than a certain amount of successes from a binomial distribution.
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| (128) |
Expectation value of a binomial distribution.
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| (129) |
Probability of measuring an event of a poisson distribution within a certain amount of time.
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| (130) |
Probability of not measuring an event of a poisson distribution within a certain amount of time.
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| (131) |
Expectation value of a poisson distribution.
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| (132) |
Probability of measuring the time between poisson events to be less than a certain value.
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| (133) |
Probability of measuring the time between poisson events to be more than a certain value.
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| (134) |
Expectation value of an exponential distribution.
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| (135) |
Probability of measuring less than a certain value for a gaussian distribution.
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| (136) |
Probability of measuring more than a certain value for a gaussian distribution.
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| (137) |
Expectation value of a gaussian distribution.
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| (138) |
Parametrization of a circle returns a parametrization of a circle.
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| (139) |
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Parametrization of an ellipse returns a parametrization of an ellipse.
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| (140) |
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Parametrization of a cycloid returns a parametrization of a cycloid.
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| (141) |
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