Singular

What is the command to make a ringed space (SpecA, OspecA)?

What do you want to calculate?

The concept of Singular , see 2.1 Background http://www.singular.uni-kl.de/Manual/la ... 3.htm#SEC5

is mainly to work mainly ideals, http://www.singular.uni-kl.de/Manual/la ... htm#SEC117

By Groebner/standardbasis computations with these ideals, you
compute invariants of the varieties defined by these ideals, e.g.
the dimension of the variety.

Operations for the varieties correspond to the well known operations on the
ideals, (cf. the alg-geom dictionary Ch 4 in Cox,Little,O'Shea)
e.g. V_1 \cup V_2 <-> I_1 * I_2 ; V_1 \cap V_2 <-> I_1 + I_2

The ring command http://www.singular.uni-kl.de/Manual/la ... htm#SEC191
declares an ambient polynomial ring.

Projective varieties are defined by homogenous ideals, see homoghttp://www.singular.uni-kl.de/Manual/latest/sing_214.htm#SEC255

Global resp. local computations are provided by global e.g. dp
resp. a local term order e.g. ds

The coordinate ring of the variety is available by the qring command:
http://www.singular.uni-kl.de/Manual/la ... htm#SEC185