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### How can I get an invertible matrix X with integral entries and AX=XB, where A and B are matrices with integral entries.

Let M be the set of all n by n matrices with integral entries. For A and B in M, how can I get an invertible matrix X in M with AX=XB in Sage.

I can partially solve that problem in GAP following method.

V={ X in Mn(QQ) | AX=XB } (V is a vector space over QQ) Basis(V)={B_1,B_2, ..., B_k} (I wonder which number k it is according to the changes of A and B.) Make X=a_1B_1 + ... +a_kB_k , a_i in some interval. Check two things which are X in Mn(ZZ) and the existence of the inverse of X in Mn(ZZ).

I can find such X for some easy matrices A,B.

How can I solve this problem in Sage?

Thanks.

### How can I get an invertible matrix X with integral entries and AX=XB, where A and B are matrices with integral entries.

Let M be the set of all n by n matrices with integral entries. For A and B in M, how can I get an invertible matrix X in M with AX=XB in Sage.

I can partially solve that problem in GAP following method.

V={ X in Mn(QQ) | AX=XB } (V is a vector space over QQ) QQ)

Basis(V)={B_1,B_2, ..., B_k} B_k} (I wonder which number k it is according to the changes of A and B.) B.)

Make X=a_1B_1 + ... +a_kB_k , a_i in some interval. interval.

Check two things which are X in Mn(ZZ) and the existence of the inverse of X in Mn(ZZ).

I can find such X for some easy matrices A,B.

How can I solve this problem in Sage?

Thanks.

### How can I get an invertible matrix X with integral entries and AX=XB, where A and B are matrices with integral entries.

Let M be the set of all n by n matrices with integral entries. entries.

For A and B in M, how can I get an invertible matrix X in M with AX=XB in Sage.

I can partially solve that problem in GAP following method.

V={ X in Mn(QQ) | AX=XB }

(V is a vector space over QQ)

Basis(V)={B_1,B_2, ..., B_k} B_k}

(I wonder which number k it is according to the changes of A and B.)

Make X=a_1B_1 + ... +a_kB_k , a_i in some interval.

Check two things which are X in Mn(ZZ) and the existence of the inverse of X in Mn(ZZ).

I can find such X for some easy matrices A,B.

How can I solve this problem in Sage?

Thanks.

### How can I get an invertible matrix X with integral entries and AX=XB, where A and B are matrices with integral entries.

Let M be the set of all n by n matrices with integral entries.

For A and B in M, how can I get an invertible matrix X in M with AX=XB in Sage.

I can partially solve that problem in GAP following method.

V={ X in Mn(QQ) | AX=XB }

(V is a vector space over QQ)

Basis(V)={B_1,B_2, ..., B_k}

(I wonder which number k it is according to the changes of A and B.)

Make X=a_1X=a_1 * B_1 + ... +a_k+a_k * B_k , a_i in some interval.

Check two things which are X in Mn(ZZ) and the existence of the inverse of X in Mn(ZZ).

I can find such X for some easy matrices A,B.

How can I solve this problem in Sage?

Thanks.

### How can I get an invertible matrix X with integral entries and AX=XB, where A and B are matrices with integral entries.

Let M be the set of all n by n matrices with integral entries.

For A and B in M, how can I get an invertible matrix X in M with AX=XB in Sage.

I can partially solve that problem in GAP following method.

V={ X in Mn(QQ) | AX=XB }

(V is a vector space over QQ)

Basis(V)={B_1,B_2, ..., B_k}

(I wonder which number k it is according to the changes of A and B.)

Make X=a_1 * B_1 + ... +a_k * B_k , a_i in some interval.interval in ZZ.

Check two things which are X in Mn(ZZ) and the existence of the inverse of X in Mn(ZZ).

I can find such X for some easy matrices A,B.

How can I solve this problem in Sage?

Thanks.

### How can I get an invertible matrix X with integral entries and AX=XB, where A and B are matrices with integral entries.

Let M be the set of all n by n matrices with integral entries.

For A and B in M, how can I get an invertible matrix X in M with AX=XB in Sage.

I can partially solve that problem in GAP following method.

• V={ X in Mn(QQ) | AX=XB }

(V is a vector space over QQ)

• Basis(V)={B_1,B_2, ..., B_k}

(I wonder which number k it is according to the changes of A and B.)

• Make X=a_1 * B_1 + ... +a_k * B_k , a_i in some interval in ZZ.

• Check two things which are X in Mn(ZZ) and the existence of the inverse of X in Mn(ZZ).

I can find such X for some easy matrices A,B.

How can I solve this problem in Sage?

Thanks.