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SolveTools[Inequality]

  

LinearUnivariateSystem

  

solve a system of linear inequalities with respect to one variable

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

LinearUnivariateSystem(sys, var)

Parameters

sys

-

system of inequalities

var

-

variable name

Description

• 

The LinearUnivariateSystem command solves a system of linear inequalities with respect to one variable.

• 

The LinearUnivariateSystem command returns a set describing the interval of possible values of the variable or a piecewise function of such sets depending on parameters

Examples

withSolveTools[Inequality]:

LinearUnivariateSystem0<x&plus;1&comma;0<2x1&comma;x

12<x

(1)

LinearUnivariateSystem0<x&plus;1&comma;2x1<0&comma;x

1<x&comma;x<12

(2)

LinearUnivariateSystemx&plus;1<0&comma;2x1<0&comma;x

x<1

(3)

LinearUnivariateSystemx&plus;1<0&comma;0<2x1&comma;x

(4)

LinearUnivariateSystemx&plus;a<0&comma;0<2x1&comma;x

&lcub;12<x&comma;x<aa<12otherwise

(5)

LinearUnivariateSystem2x&plus;a0&comma;02xb&comma;x

&lcub;x12a&comma;12bxabotherwise

(6)

LinearUnivariateSystemax&plus;20&comma;02xb&comma;x

&lcub;x2a&comma;12bxAnd0<a&comma;12b2a2axAnda<0&comma;12b<2a12bxAnda<0&comma;2a12ba&equals;0otherwise

(7)

LinearUnivariateSystemax&plus;b<0&comma;0cx&plus;d&comma;x

&lcub;xdcAnd0<a&comma;c<0&comma;dc<bax<baAnd0<a&comma;c<0&comma;badcdcx&comma;x<baAnd0<a&comma;0<c&comma;dc<bax<baAnd0<a&comma;c&equals;0&comma;0dAnd0<a&comma;c&equals;0&comma;d<0xdc&comma;ba<xAnda<0&comma;c<0&comma;ba<dcdcxAnda<0&comma;0<c&comma;ba<dcba<xAnda<0&comma;0<c&comma;dcbaba<xAnda<0&comma;c&equals;0&comma;0dAnda<0&comma;c&equals;0&comma;d<0xdcAnda&equals;0&comma;b<0&comma;c<0dcxAnda&equals;0&comma;b<0&comma;0<cxAnda&equals;0&comma;b<0&comma;c&equals;0&comma;0dAnda&equals;0&comma;b<0&comma;c&equals;0&comma;d<0Anda&equals;0&comma;0b

(8)

See Also

SolveTools

SolveTools[Inequality][LinearMultivariateSystem]

SolveTools[Inequality][LinearUnivariate]

 


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