from the theory of proveit.physics.quantum.algebra¶

In [1]:
import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
# import Expression classes needed to build the expression
from proveit import Conditional, Lambda
from proveit.linear_algebra import ScalarMult
from proveit.logic import Equals, InSet
from proveit.physics.quantum import Qmult, bra_varphi, ket_varphi, var_ket_psi, var_ket_v, varphi
from proveit.physics.quantum.algebra import Hspace
In [2]:
# build up the expression from sub-expressions
expr = Lambda(varphi, Conditional(Equals(Qmult(var_ket_psi, bra_varphi), Lambda(var_ket_v, Conditional(ScalarMult(Qmult(bra_varphi, var_ket_v), var_ket_psi), InSet(var_ket_v, Hspace)))), InSet(ket_varphi, Hspace)))
Out[2]:
expr:
In [3]:
# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")
Passed sanity check: expr matches stored_expr
In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
\varphi \mapsto \left\{\left(\lvert \psi \rangle \thinspace \langle \varphi \rvert\right) = \left[\lvert v \rangle \mapsto \left\{\left(\langle \varphi \rvert \thinspace \lvert v \rangle\right) \cdot \lvert \psi \rangle \textrm{ if } \lvert v \rangle \in \mathcal{H}\right..\right] \textrm{ if } \lvert \varphi \rangle \in \mathcal{H}\right..
In [5]:
stored_expr.style_options()
Out[5]:
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
Out[6]:
core typesub-expressionsexpression
0Lambdaparameter: 29
body: 1
1Conditionalvalue: 2
condition: 3
2Operationoperator: 4
operands: 5
3Operationoperator: 18
operands: 6
4Literal
5ExprTuple7, 8
6ExprTuple9, 22
7Operationoperator: 23
operands: 10
8Lambdaparameter: 26
body: 12
9Operationoperator: 13
operand: 29
10ExprTuple21, 25
11ExprTuple26
12Conditionalvalue: 14
condition: 15
13Literal
14Operationoperator: 16
operands: 17
15Operationoperator: 18
operands: 19
16Literal
17ExprTuple20, 21
18Literal
19ExprTuple26, 22
20Operationoperator: 23
operands: 24
21Variable
22Variable
23Literal
24ExprTuple25, 26
25Operationoperator: 27
operand: 29
26Variable
27Literal
28ExprTuple29
29Variable