1 | initial version |

The code of `minimize_constrained`

starts checking if the first argument is a symbolic expression. If this were the case, it gets the variables on which such an expression depends. Then the code generates a function whose argument is a vector, needed for any subsequent computation; each variable of the expression is replaced by a component of the vector. For example, if the expression is `x^2+y`

, the variables are `x`

and `y`

. The code defines a function whose argument is a vector, say `p`

, which yields `p[0]^2+p[1]`

.

When $f(x,y)=x$, the expression `f(x,y)`

has only one variable, which is `x`

, and so the function defined inside `minimize_constrained`

does not depend on a vector with two components, as required, raising errors.

To use `minimize_constrained`

, I would advise to directly define Python functions depending on vectors, either with `def`

or `lambda`

. For example, for $f(x,y)=x+y$, we can write

```
def f(x): return x[0] + x[1]
def c(x): return 1 - x[0]^2 - x[1]^2
```

or also

```
f = lambda x: x[0] + x[1]
c = lambda x: 1 - x[0]^2 - x[1]^2
```

In both cases, we get:

```
sage: minimize_constrained(f, c, [0,0])
(-0.7071774954004159, -0.7070360740443554)
```

Likewise,

```
sage: f = lambda x: x[0]
sage: c = lambda x: 1 - x[0]^2 - x[1]^2
sage: minimize_constrained(f, c, [0,0])
(-1.0000000049989504, 9.999999987505248e-05)
```

which is the expected result.

If, for clarity, you prefer to explicitly define functions in terms of `x`

and `y`

, you can still do that:

```
sage: f = lambda x,y: x
sage: c = lambda x,y: 1 - x^2 - y^2
sage: ff = lambda p: f(*p)
sage: cc = lambda p: c(*p)
sage: minimize_constrained(ff, cc, [0,0])
(-1.0000000049989504, 9.999999987505248e-05)
```

2 | No.2 Revision |

The code of `minimize_constrained`

starts checking if the first argument is a symbolic expression. If this were the case, it gets the variables on which such an expression depends. Then the code generates a function whose argument is a vector, needed for any subsequent computation; each variable of the expression is replaced by a component of the vector. For example, if the expression is `x^2+y`

, the variables are `x`

and `y`

. The code defines a function whose argument is a vector, say `p`

, which yields `p[0]^2+p[1]`

.

When $f(x,y)=x$, the expression `f(x,y)`

has only one variable, which is `x`

, and so the function defined inside `minimize_constrained`

does not depend on a vector with two components, as required, raising errors.

To use `minimize_constrained`

, I would advise to directly define Python functions depending on vectors, either with `def`

or `lambda`

. For example, for $f(x,y)=x+y$, we can write

```
def f(x): return x[0] + x[1]
def c(x): return 1 - x[0]^2 - x[1]^2
```

or also

```
f = lambda x: x[0] + x[1]
c = lambda x: 1 - x[0]^2 - x[1]^2
```

In both cases, we get:

```
sage: minimize_constrained(f, c, [0,0])
(-0.7071774954004159, -0.7070360740443554)
```

Likewise, for $f(x,y)=x$, we have:

```
sage: f = lambda x: x[0]
sage: c = lambda x: 1 - x[0]^2 - x[1]^2
sage: minimize_constrained(f, c, [0,0])
(-1.0000000049989504, 9.999999987505248e-05)
```

which is the expected result.

If, for clarity, you prefer to explicitly define functions in terms of `x`

and `y`

, you can still do that:

```
sage: f = lambda x,y: x
sage: c = lambda x,y: 1 - x^2 - y^2
sage: ff = lambda p: f(*p)
sage: cc = lambda p: c(*p)
sage: minimize_constrained(ff, cc, [0,0])
(-1.0000000049989504, 9.999999987505248e-05)
```

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