# Missing solution in homogeneous equation

```
var('x y')
solve(x*y, [x, y])
```

returns only the solution x=0, missing y=0. Is this a known bug? I am using sage 5.13.

1

First, the workaround.

```
sage: var('y')
y
sage: a = x*y
sage: solve([a,1==1],[x,y])
[[x == r1, y == 0], [x == 0, y == r2]]
```

There is an open ticket about this I will try to find later. But at least now I know the reason.

This is interesting - apparently we assume that if one passes in a single expression, there is a single variable that should be solved for.

```
# There *should* be only one variable in the list, since it is
# passed from sage.symbolic.relation.solve() and multiple variables
# there don't call this function.
if isinstance(x, (list, tuple)):
x = x[0]
```

That explains your result. However, @moroplogo's is even more interesting. What happens is that all arguments get passed to `xy.solve()`

```
if is_Expression(f): # f is a single expression
ans = f.solve(*args,**kwds)
return ans
```

But these are *not* unpacked! So we have something that actually passes in to Maxima. But what? It's not passing in this:

```
(%i2) solve(x*y,[x,y]);
(%o2) [[x = %r1, y = 0], [x = 0, y = %r2]]
```

and some debugging indicates it should just be passing in the same as `solve(x*y,x)`

. I'm not sure how that extra `[1]`

gets in there.

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Asked: ** 2014-02-12 04:45:46 +0200 **

Seen: **435 times**

Last updated: **Feb 14 '14**

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It's a strange problem indeed! However this is not a well-formed code , you can write this : solve([x*y==0], x , y) and the answer is : ([x == 0], [1]) . If you write this : solve([x*y==0], y ,x) the answer is : ([y == 0], [1]) .