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[[Algebra]] ([[French]]: ''[[algèbre]]'') is a branch of [[mathematics]] which reduces the solution of problems to manipulations of symbolic expressions. Lacan begins to use algebraic symbols in his work in 1955 (see [[schema Lsymbolic]]), in an attempt to formalise psychoanalysisexpressions. Three main reasons lie behind this attempt at formalisation:

1. Formalisation is necessary for psychoanalysis [[Lacan]] begins to acquire scientific status (see use [[algebraic]] [[sciencesymbol]]). Just as s in his work in 1955 (see [[Claude Lévi-Straussschema L]] uses quasi-mathematical formulae ), in an attempt to set anthropology on a more scientific footing, Lacan attempts to do the same for [[formalise]] [[psychoanalysis]].

31. [[Formalisation of psychoanalytic theory in terms of algebraic symbols ]] is a means of preventing intuitive understanding, which Lacan regards as an imaginary lure which hinders access necessary for [[psychoanalysis]] to the symbolicacquire [[scientific]] status. Rather than being understood in an intuitive way, the algebraic symbols are to be used, manipulated and read in various different ways.<ref>see E, 313</ref>

Most English translations of Lacan also translate the algebraic symbols which appear in his work. For example, Alan Sheridan, Just as [[Claude Lévi-Strauss]] uses quasi-mathematical formulae in his translation of Ecrits, renders the symbol A (for Autre) as O (for Other). However, Lacan was opposed an attempt to such set [[anthropology]] on a practice, as Sheridan himself points out.<ref>Sheridan, 1977: xi</ref>In this dictionarymore [[scientific]] footing, in line with [[Lacan's own preference, ]] attempts to do the algebraic symbols are left as they are in the original French textssame for [[psychoanalysis]].

2. [[Formalisation]] can provide a core of [[psychoanalytic theory]] which can be transmitted integrally even to those who have never experienced [[psychoanalytic]] [[treatment]].  The [[formulae]] thus become an essential aspect of the [[training]] of [[psychoanalysts]] which take their place alongside the [[training]] [[analysis]] as a medium for the transmission of [[psychoanalytic]] [[knowledge]]. 3. [[Formalisation]] of [[psychoanalytic theory]] in terms of [[algebraic ]] symbols is a means of preventing intuitive understanding, which [[Lacan]] regards as an [[imaginary]] [[lure]] which hinders access to the [[symbolic]].  Rather than being understood in an intuitive way, the [[algebraic]] [[symbol]]s are to be used, manipulated and read in various different ways.<ref>{{E}} p.313</ref>  Most English translations of [[Lacan]] also translate the [[algebraic]] [[symbol]]s which appear in his work.  For example, [[Alan Sheridan]], in his translation of [[Ecrits]], renders the [[symbol]] A (for [[Autre]]) as O (for [[Other]]).  However, [[Lacan]] was opposed to such a [[practice]], as [[Sheridan]] himself points out.<ref>Sheridan, 1977: xi</ref> In this dictionary, in line with [[Lacan]]'s own preference, the [[algebraic]] [[symbol]]s are left as they are in the original [[French]] texts.  The [[algebraic]] [[symbol]]s used by [[Lacan]], which appear principally in the MATHEMES[[matheme]]s, SCHEMA L [[schema l]] and the GRAPH OF DESIRE[[graph of desire]], are listed below, together with their most common [[meaning]].  However, it is important to remember that the symbols [[symbol]]s do not always refer to the same concept throughout [[Lacan]]'s work, but are used in different ways as his work develops.  The most important example of such a shift in meaning is the use of the [[symbol ]] a, which is used in radically different ways in the 1950s and in the 1960s.  However, even other symbols [[symbol]]s which are relatively stable in [[meaning ]] are occasionally used in very different ways; for example, s nearly always designates the signified, but is used in one algorithm to denote the [[subject supposed to know (see ]].<ref>Lacan, 1967). </ref> Therefore some caution should be exercised when referring to the following list of equivalences.  A = the big Other A = the barred Other a = (see objet petit a) a' = (see objet petit a) S =

 S = the barred subjectSi 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) =  

I = the ego-ideal (schema R) I(A) = the ego-ideal (graph of desire) H = the real phallus <fi = the symbolic phallus [upper-case phi] 9 = the imaginary phallus [lower-case 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/Name-of-the-Father 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) The typographical details and diacritics are extremely important in Lacanian algebra.  The difference between upper- and lower-case symbols[[symbol]]s, the difference between italicised and non-italicised symbols[[symbol]]s, the use of the apostrophe, the minus [[sign]], and subscripts; all these details play their part in the [[algebraic ]] system.  For example the upper-case letters usually refer to the [[symbolic ]] [[order]], whereas the lower-case letters usually refer to the [[imaginary]].  The use of the [[bar ]] is also important, and varies even within the same formula.