### The Maxima on-line user's manual

Algebra Calculator

#### Riemann

Function: riemann (<dis>) A function in the `ctensor` (component tensor) package. `riemann` computes the Riemann curvature tensor from the given metric and the corresponding Christoffel symbols. The following index conventions are used:

l _l _l _l _m _l _m R[i,j,k,l] = R = | - | + | | - | | ijk ij,k ik,j mk ij mj ik

This notation is consistent with the notation used by the `itensor` package and its `icurvature` function. If the optional argument <dis> is `true`, the non-zero components `riem[i,j,k,l]` will be displayed. As with the Einstein tensor, various switches set by the user control the simplification of the components of the Riemann tensor. If `ratriemann` is `true`, then rational simplification will be done. If `ratfac` is `true` then each of the components will also be factored.

If the variable `cframe_flag` is `false`, the Riemann tensor is computed directly from the Christoffel-symbols. If `cframe_flag` is `true`, the covariant Riemann-tensor is computed first from the frame field coefficients.

There are also some inexact matches for `riemann`. Try `?? riemann` to see them.

```(%o1)                                true
(%i2) ```

### Related Examples

##### riemann

riemann;

-dt^2+a(t)^2*(dr^2/(1...

Calculate

##### riemann-sin

riemann;

-dt^2+ sin(1/x^2)*dx^...

Calculate

##### riemann

riemann;

-r^2*dt^2 + dr^2=0;

Calculate

##### riemann-true

riemann(true);

f(x)*dx^2 + dy^2;

Riemann(true);

Calculate

##### riemann

riemann;

x* dx^2 + dy^2 + dz^2...

Calculate

##### riemann

riemann;

dx^2 + dy^2 + dz^2;

Calculate

##### riemann

riemann;

dx^2 + dy^2=ds^2;

Calculate

##### riemann-sin-true

riemann(true);

da^2 + sin(a)^2 * (d...

Calculate

##### riemann

riemann;

2*dudv + a^2*dw^2 + b...

Calculate

##### riemann

riemann;

N(t,x)^2*dt^2 - dx^2...

Calculate