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.
# import Expression classes needed to build the expression
from proveit import e, l
from proveit.logic import Equals, InSet
from proveit.numbers import Add, Interval, Neg, one, subtract
from proveit.physics.quantum.QPE import _neg_domain, _two_pow__t_minus_one

In [2]:
# build up the expression from sub-expressions
expr = Equals(InSet(l, _neg_domain), InSet(l, Interval(Add(Neg(_two_pow__t_minus_one), one), subtract(Neg(e), one))))

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())

\left(l \in \{-2^{t - 1} + 1~\ldotp \ldotp~-\left(e + 1\right)\}\right) = \left(l \in \{-2^{t - 1} + 1~\ldotp \ldotp~-e - 1\}\right)

In [5]:
stored_expr.style_options()

namedescriptiondefaultcurrent valuerelated methods
operation'infix' or 'function' style formattinginfixinfix
wrap_positionsposition(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.()()('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'centercenter('with_justification',)
directionDirection of the relation (normal or reversed)normalnormal('with_direction_reversed', 'is_reversed')
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0Operationoperator: 1
operands: 2
1Literal
2ExprTuple3, 4
3Operationoperator: 6
operands: 5
4Operationoperator: 6
operands: 7
5ExprTuple9, 8
6Literal
7ExprTuple9, 10
8Operationoperator: 12
operands: 11
9Variable
10Operationoperator: 12
operands: 13
11ExprTuple15, 14
12Literal
13ExprTuple15, 16
14Operationoperator: 36
operand: 20
15Operationoperator: 32
operands: 18
16Operationoperator: 32
operands: 19
17ExprTuple20
18ExprTuple21, 38
19ExprTuple22, 35
20Operationoperator: 32
operands: 23
21Operationoperator: 36
operand: 26
22Operationoperator: 36
operand: 27
23ExprTuple27, 38
24ExprTuple26
25ExprTuple27
26Operationoperator: 28
operands: 29
27Variable
28Literal
29ExprTuple30, 31
30Literal
31Operationoperator: 32
operands: 33
32Literal
33ExprTuple34, 35
34Literal
35Operationoperator: 36
operand: 38
36Literal
37ExprTuple38
38Literal