## Equations

## Main.Equations History

Hide minor edits - Show changes to output

Changed lines 28-29 from:

|| log10 ||Base-10 Log || log10(x*y)=0 ||

|| log ||Natural Log || log(x*y)=0 ||

|| log ||Natural Log || log(x*y)=0 ||

to:

|| log10() ||Base-10 Log || log10(x*y)=0 ||

|| log() ||Natural Log || log(x*y)=0 ||

|| log() ||Natural Log || log(x*y)=0 ||

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|| tanh() ||Hyperbolic ~~Tanget~~ || tanh(x*y)=0 ||

to:

|| tanh() ||Hyperbolic Tangent || tanh(x*y)=0 ||

Added lines 43-44:

All trigonometric functions are in radians (not degrees).

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The available operands are listed below with a short description of each and a simple example involving variable ''x'' and ''y''. Equations may be in the form of ~~equalities~~ (=) or ~~inequalities~~ (>,<). For inequalities, the equation may be bounded between lower and upper limits that are also functions of variables.

to:

The available operands are listed below with a short description of each and a simple example involving variable ''x'' and ''y''. Equations may be in the form of equality (=) or inequality (>,>=,<,<=) constraints. For inequalities, the equation may be bounded between lower and upper limits that are also functions of variables.

Changed line 9 from:

The available operands are listed below with a short description of each and a simple example involving variable ''x'' and ''y''. ~~For equations~~ may be in the form of equalities (=) or inequalities (>,<). For inequalities, the equation may be bounded between lower and upper limits that are also functions of variables.

to:

The available operands are listed below with a short description of each and a simple example involving variable ''x'' and ''y''. Equations may be in the form of equalities (=) or inequalities (>,<). For inequalities, the equation may be bounded between lower and upper limits that are also functions of variables.

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(:table border=1 width=~~50~~% align=left bgcolor=#EEEEEE cellspacing=0:)

to:

(:table border=1 width=100% align=left bgcolor=#EEEEEE cellspacing=0:)

Deleted lines 21-23:

|| - ||Unary minus || -(x-y) = 0 ||

|| - ||Unary minus || -(x-y) = 0 ||

Changed lines 70-72 from:

(y+2/x)^(x*z) * (log(tanh(sqrt(y-x+x^2))+3))^2 = 2+sinh(y)+acos(x+y)+asin(x/y)

to:

(y+2/x)^(x*z) * &

(log(tanh(sqrt(y-x+x^2))+3))^2 &

= 2+sinh(y)+acos(x+y)+asin(x/y)

(log(tanh(sqrt(y-x+x^2))+3))^2 &

= 2+sinh(y)+acos(x+y)+asin(x/y)

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to:

The available operands are listed below with a short description of each and a simple example involving variable ''x'' and ''y''. For equations may be in the form of equalities (=) or inequalities (>,<). For inequalities, the equation may be bounded between lower and upper limits that are also functions of variables.

Changed line 15 from:

|| !,#,% ||Comment ||~~!!~~ equation #1 (:html:)<br>(:htmlend:) 0 = x[1] + x[2] ! ~~comment~~ ||

to:

|| !,#,% ||Comment ||% equation #1 (:html:)<br>(:htmlend:) 0 = x[1] + x[2] ! eqn1 ||

Changed line 15 from:

|| !,#,% ||Comment ||~~ ~~! equation #1 (:html:)<br>(:htmlend:) 0 = x[1] + x[2] ! comment ||

to:

|| !,#,% ||Comment ||!! equation #1 (:html:)<br>(:htmlend:) 0 = x[1] + x[2] ! comment ||

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|| !,#,% ||Comment || ! comment ||

to:

|| !,#,% ||Comment || ! equation #1 (:html:)<br>(:htmlend:) 0 = x[1] + x[2] ! comment ||

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|| border=1 width=~~50~~%

to:

|| border=1 width=80%

Changed lines 15-17 from:

|| ~~=~~ ||Line Continuation || 0 = x[1] & (:html:)<br>(:htmlend:) + x[2] ||

to:

|| !,#,% ||Comment || ! comment ||

|| = ||Equality || x=y ||

|| & ||Line Continuation || 0 = x[1] & (:html:)<br>(:htmlend:) + x[2] ||

|| = ||Equality || x=y ||

|| & ||Line Continuation || 0 = x[1] & (:html:)<br>(:htmlend:) + x[2] ||

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|| = ||Line Continuation || 0 = x[1] & ~~\n~~ + x[2] ||

to:

|| = ||Line Continuation || 0 = x[1] & (:html:)<br>(:htmlend:) + x[2] ||

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|| border=1 width=~~30~~%

to:

|| border=1 width=50%

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|| = ||Line Continuation || 0 = x[1] & \n + x[2] ||

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|| erf() ||Error function || erf(x*y)=0 ||

|| erfc() ||Complementary error function || erfc(x*y)=0 ||

|| erfc() ||Complementary error function || erfc(x*y)=0 ||

Changed lines 11-12 from:

There are currently ~~21~~ operands for parameters or variables. They are listed below with a short description of each and a simple example involving variable ''x'' and ''y''.

to:

There are currently 26 operands for parameters or variables. They are listed below with a short description of each and a simple example involving variable ''x'' and ''y''. For equations may be in the form of equalities (=) or inequalities (>,<). For inequalities, the equation may be bounded between lower and upper limits that are also functions of variables.

Added lines 15-19:

|| = ||Equality || x=y ||

|| < ||Less than || x<y ||

|| <= ||Less than or equal || x<=y ||

|| > ||Greater than || x>y ||

|| >= ||Greater than or equal || x>=y ||

|| < ||Less than || x<y ||

|| <= ||Less than or equal || x<=y ||

|| > ||Greater than || x>y ||

|| >= ||Greater than or equal || x>=y ||

Added lines 21-23:

|| - ||Unary minus || -(x-y) = 0 ||

|| - ||Unary minus || -(x-y) = 0 ||

|| - ||Unary minus || -(x-y) = 0 ||

|| - ||Unary minus || -(x-y) = 0 ||

|| - ||Unary minus || -(x-y) = 0 ||

Changed lines 47-48 from:

A couple differential and algebraic equations are shown below~~. The steady-state solution is p=2, x=-1.0445, y=0.1238, and z=-1.0445~~. For steady-state solutions the differential variables (''$x'') are set to zero. Variables x, y, and z were not given initial values. In the absence of an initial condition, variables are set to a default value of 1.0.

to:

A couple differential and algebraic equations are shown below. For steady-state solutions the differential variables (''$x'') are set to zero. Variables x, y, and z were not given initial values. In the absence of an initial condition, variables are set to a default value of 1.0.

Changed line 51 from:

! Example ~~model that demonstrates a few~~ equations

to:

! Example with three equality equations

Added lines 69-92:

The steady-state solution is:

p=2

x=-1.0445

y=0.1238

z=-1.0445.

(:cellnr:)

! Example with an inequality

Model example

Variables

x

y

z

End Variables

Equations

x = 0.5 * y

0 = z + 2*x

x < y < z

End Equations

End Model

Changed lines 41-62 from:

(:table ~~class~~=~~'markup horiz' align~~=~~'~~left~~':)~~

(:cellnr class=~~'markup1'~~:)

~~>>blue<<~~

[@! Example model that demonstrates a few equations

Model example

Parameters

p = 2

End Parameters

Variables

x

y

z

End Variables

Equations

exp(x*p)=y

z = p*$x + x

(y+2/x)^(x*z) * (log(tanh(sqrt(y-x+x^2))+3))^2 = 2+sinh(y)+acos(x+y)+asin(x/y)

End Equations

End~~Model@]~~

>><<

(:cellnr class

[@!

Model example

Parameters

p = 2

End Parameters

Variables

x

y

z

End Variables

Equations

exp(x*p)=y

z = p*$x + x

(y+2/x)^(x*z) * (log(tanh(sqrt(y-x+x^2))+3))^2 = 2+sinh(y)+acos(x+y)+asin(x/y)

End Equations

End

>><<

to:

(:table border=1 width=50% align=left bgcolor=#EEEEEE cellspacing=0:)

(:cellnr:)

! Example model that demonstrates a few equations

Model example

Parameters

p = 2

End Parameters

Variables

x

y

z

End Variables

Equations

exp(x*p)=y

z = p*$x + x

(y+2/x)^(x*z) * (log(tanh(sqrt(y-x+x^2))+3))^2 = 2+sinh(y)+acos(x+y)+asin(x/y)

End Equations

End Model

(:cellnr:)

! Example model that demonstrates a few equations

Model example

Parameters

p = 2

End Parameters

Variables

x

y

z

End Variables

Equations

exp(x*p)=y

z = p*$x + x

(y+2/x)^(x*z) * (log(tanh(sqrt(y-x+x^2))+3))^2 = 2+sinh(y)+acos(x+y)+asin(x/y)

End Equations

End Model

Changed lines 9-10 from:

!!! ~~Equation operands~~

to:

!!! Operations

Changed line 37 from:

!!!~~ Equation~~ Example

to:

!!! Example