# Revision history [back]

### Ideals of non-commutative polynomials

Basically I have the same question as here, but in the non-commutative case: Given non-commutative multi-variate polynomials $f_1,\dotsc,f_s$, how can I test (with sage, or any other program which can do this) that $g \in \langle f_1,\dotsc,f_s \rangle$ (two-sided ideal) and find an explicit linear combination $g = \sum_i a_i f_i b_i$ which demonstrates this?

There is a patch which somehow contains the necessary functions, but unfortunately I don't know how to use/install this patch. Also the help pages only confuse me. Can someone explain this in easy steps? Sorry for this stupid question ...

### Ideals of non-commutative polynomials

Basically I have the same question as here, but in the non-commutative case: Given non-commutative multi-variate polynomials $f_1,\dotsc,f_s$, how can I test (with sage, or any other program which can do this) that $g \in \langle f_1,\dotsc,f_s \rangle$ (two-sided ideal) and find an explicit linear combination $g = \sum_i a_i f_i b_i$ which demonstrates this?

There is a patch which somehow contains the necessary functions, but unfortunately I don't know how to use/install this patch. Also the help pages only confuse me. Can someone explain this in easy steps? Sorry for this stupid question ...

EDIT: Ok this installation was already explained here.

### Ideals of non-commutative polynomials

Basically I have the same question as here, but in the non-commutative case: Given non-commutative multi-variate polynomials $f_1,\dotsc,f_s$, how can I test (with sage, or any other program which can do this) that $g \in \langle f_1,\dotsc,f_s \rangle$ (two-sided ideal) and find an explicit linear combination $g = \sum_i a_i f_i b_i$ which demonstrates this?

There is a patch which somehow contains the necessary functions, but unfortunately I don't know how to use/install this patch. Also the help pages only confuse me. Can someone explain this in easy steps? Sorry for this stupid question ...

EDIT: Ok this installation was already explained here.. But I am using the sage notebook (and don't know how to use the command line, sorry).

### Ideals of non-commutative polynomials

Basically I have the same question as here, but in the non-commutative case: Given non-commutative multi-variate polynomials $f_1,\dotsc,f_s$, how can I test (with sage, or any other program which can do this) that $g \in \langle f_1,\dotsc,f_s \rangle$ (two-sided ideal) and find an explicit linear combination $g = \sum_i a_i f_i b_i$ which demonstrates this?

There is a patch which somehow contains the necessary functions, but unfortunately I don't know how to use/install this patch. Also the help pages only confuse me. Can someone explain this in easy steps? Sorry for this stupid question ...

EDIT: Ok this installation was already explained here. But actually it is already included in the newest version of Sage, which I am using the sage notebook (and have updated. But I still don't know how to use the command line, sorry).functions.

### Ideals of non-commutative polynomials

Basically I have the same question as here, but in the non-commutative case: Given non-commutative multi-variate polynomials $f_1,\dotsc,f_s$, $f_1,\dotsc,f_s \in \mathbb{Q}\langle x_1,\dotsc,x_n \rangle$, how can I test (with sage, or any other program which can do this) that some $g \in \mathbb{Q}\langle x_1,\dotsc,x_n \rangle$ satisfies $g \in \langle f_1,\dotsc,f_s \rangle$ (two-sided ideal) ideal), and find an explicit linear combination $g = \sum_i a_i f_i b_i$ which demonstrates this?

There is a In trac ticket patch#11068 which somehow contains non-commutative quotient rings were implemented. However, according to the necessary functions, but unfortunately I don't know reference manual on quotient rings, this assumes that one defines a reduce method by hand. But in my example , it is not clear how to use/install this patch. Also the help pages only confuse me. Can someone explain this in easy steps? Sorry for this stupid question ...

EDIT: Ok this installation was already explained here. But actually it is already included in the newest version of Sage, which I have updated. But I still don't know how to use the functions.do this.