# Symbolic equivalence

Hi all,

I define ;

```
sage: x,y,z=var("x y z")
sage: x=y+z
sage: x
y + z
sage: y
y
```

I want to achieve the following:

```
sage: y
x-z
```

any idea how this scenario would be possible ?

Symbolic equivalence

asked
**
2015-04-19 11:06:05 -0500
**

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Hi all,

I define ;

```
sage: x,y,z=var("x y z")
sage: x=y+z
sage: x
y + z
sage: y
y
```

I want to achieve the following:

```
sage: y
x-z
```

any idea how this scenario would be possible ?

1

Use an equation to encode the relations between the variables.

You can then solve the equation with respect to the variable of your choice.

An example:

```
sage: x,y,z = var('x y z')
sage: eq = x==y+z
sage: solve(eq, x)
[x == y + z]
sage: solve(eq, y)
[y == x - z]
```

Asked: **
2015-04-19 11:06:05 -0500
**

Seen: **317 times**

Last updated: **Jul 15 '15**

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I do not think I understand your question, but note you have

`sage: bool(y == x-z)`

that evaluates to`True`

I do not understand what you exactly mean by "I want to achieve ...".What I tried to mean is that when I query for "y" I want to get the corresponding equivalence. I want to construct the equations in such a way that Sage will be aware of this. Bool works but not exactly what I want.