Algebra
Algebra (French: algèbre) is a branch of mathematics which reduces the solution of problems to manipulations of symbolic expressions.
Formalisation can provide a core of psychoanalytic theory.
The formulae thus become a medium for the transmission of psychoanalytic knowledge.
Formalization
Jacques Lacan begins to use algebraic symbols in 1955 (in an attempt to formalise psychoanalysis).
Jacques Lacan attempted to formalize psychoanalytic theory in terms of algebraic symbols.
Lacan used quasimathematical formulae in an attempt to set psychoanalysis on a more scientific footing.
Formalisation is necessary for psychoanalysis to acquire scientific status.
The algebraic symbols are to be used, manipulated and read in various different ways.^{[1]}
Details
The difference between upper and lowercase symbols, the difference between italicised and nonitalicised symbols, the use of the apostrophe, the minus sign, and subscripts.
For example the uppercase letters usually refer to the symbolic order, whereas the lowercase letters usually refer to the imaginary.
The use of the bar is also important.
His use of algebraic formulations is in fact unconnected to mathematics itself, but merely provides a concise way of expressing complex psychoanalytic concepts.
a generalization of arithmetic in which letters representing numbers are combined a branch of mathematics in which symbols, usually letters of the alphabet, represent numbers or members of a specified set and are used to represent quantities and to express general relationships that hold for all members of the set.
The algebraic symbols used by Lacan, which appear principally in the mathemes, schema l and the graph of desire, are listed below, together with their most common meaning.
The symbols do not always refer to the same concept throughout Lacan's work, but are used in different ways as his work develops.
Therefore some caution should be exercised when referring to the following list of equivalences.
Even other symbols which are relatively stable in meaning are occasionally used in very different ways.
Algebra
SYMBOL  TRANSLATION 

A  the big Other 
the barred Other  
a  (see objet petit a 
a'  (see objet petit a 
1. (before 1957) the subject 2.(from 1957 on) the signifier 3. (in the schemas of Sade) the raw subject of pleasure  
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the barred subject 
the barred subject  
the master signifier  
the signifying chain/knowledge  
the signified (in the Saussurean algorithm  
D  Demand 
d  Desire 
A = the big Other
A = the barred Other
a = (see objet petit a)
a' = (see objet petit a)
S =
1. (before 1957) the subject
2. (from 1957 on) the signifier
3. (in the schemas of Sade) the raw subject of pleasure
S = the barred subject
S1 = the master signifier
S2 = the signifying chain/knowledge
s = the signified (in the Saussurean algorithm)
S(A) = the signifier of a lack in the Others
(A) = the signification of the Other (the messagelsymptom)
D = demand
d = desire
m = the ego (moi)
i = the specular image (schema R)
i(a) =
1. the specular image (graph of desire)
2. the ideal ego (optical model)
I = the egoideal (schema R)
I(A) = the egoideal (graph of desire)
H = the real phallus
<? = the symbolic phallus [uppercase phi]
9 = the imaginary phallus [lowercase phi]
(9) = castration [minus phi]
S = the symbolic order (schema R)
R = the field of reality (schema R)
I = the imaginary order (schema R)
P = the symbolic father/NameoftheFather
p = the imaginary father
M = the symbolic mother
J = jouissance
Je = phallic jouissance
JA = the jouissance of the other
E = the statement
e = the enunciation
V = the will to enjoy (volontÈ de jouissance)
References
 ↑ Lacan, Jacques. Écrits: A Selection. Trans. Alan Sheridan. London: Tavistock Publications, 1977. p.313