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Expression of type Forall

from the theory of proveit.physics.quantum.QPE

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.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import l
from proveit.linalg import MatrixProd
from proveit.logic import Equals, Forall
from proveit.numbers import Integer
from proveit.physics.quantum import Ket, RegisterBra
from proveit.physics.quantum.QPE import ModAdd, Psi_, alpha_l, b_, t_
In [2]:
# build up the expression from sub-expressions
expr = Forall([l], Equals(alpha_l, MatrixProd(RegisterBra(ModAdd(b_, l), t_), Ket(Psi_))), domain = Integer)
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(expr.latex())
\forall_{l \in \mathbb{Z}}~\left(\alpha_{l} = {_{t}}\langle b \oplus l \rvert\Psi \rangle\right)
In [5]:
expr.style_options()
Out[5]:
namedescriptiondefaultcurrent valuerelated methods
with_wrappingIf 'True', wrap the Expression after the parametersNoneNone/False('with_wrapping',)
wrap_paramsIf 'True', wraps every two parameters AND wraps the Expression after the parametersNoneNone/False('with_params',)
justificationjustify to the 'left', 'center', or 'right' in the array cellscentercenter('with_justification',)
In [6]:
# display the expression information
expr.expr_info()
Out[6]:
 core typesub-expressionsexpression
0Operationoperator: 1
operand: 3
1Literal
2ExprTuple3
3Lambdaparameter: 31
body: 4
4Conditionalvalue: 5
condition: 6
5Operationoperator: 7
operands: 8
6Operationoperator: 9
operands: 10
7Literal
8ExprTuple11, 12
9Literal
10ExprTuple31, 13
11Operationoperator: 14
operands: 15
12Operationoperator: 16
operands: 17
13Literal
14Literal
15ExprTuple18, 31
16Literal
17ExprTuple19, 20
18Literal
19Operationoperator: 21
operands: 22
20Operationoperator: 23
operand: 27
21Literal
22ExprTuple25, 26
23Literal
24ExprTuple27
25Operationoperator: 28
operands: 29
26Literal
27Literal
28Literal
29ExprTuple30, 31
30Literal
31Variable