# 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
from proveit.logic import And
from proveit.numbers import Add, Less, LessEq, Neg, one
from proveit.physics.quantum.QPE import _two_pow__t_minus_one

In [2]:
# build up the expression from sub-expressions
sub_expr2 = Neg(sub_expr1)
expr = And(LessEq(Add(Neg(_two_pow__t_minus_one), one), sub_expr2), Less(sub_expr2, sub_expr1), LessEq(sub_expr1, _two_pow__t_minus_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(\left(-2^{t - 1} + 1\right) \leq \left(-\left(e + 1\right)\right)\right) \land \left(\left(-\left(e + 1\right)\right) < \left(e + 1\right)\right) \land \left(\left(e + 1\right) \leq 2^{t - 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',)
as_total_orderingWhen 'True', style the conjunction as a total ordering (e.g. x < y < z from (x < y) and (y < z))NoneNone/False('with_total_ordering_style',)
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0Operationoperator: 1
operands: 2
1Literal
2ExprTuple3, 4, 5
3Operationoperator: 9
operands: 6
4Operationoperator: 7
operands: 8
5Operationoperator: 9
operands: 10
6ExprTuple11, 12
7Literal
8ExprTuple12, 16
9Literal
10ExprTuple16, 19
11Operationoperator: 25
operands: 13
12Operationoperator: 29
operand: 16
13ExprTuple15, 31
14ExprTuple16
15Operationoperator: 29
operand: 19
16Operationoperator: 25
operands: 18
17ExprTuple19
18ExprTuple20, 31
19Operationoperator: 21
operands: 22
20Variable
21Literal
22ExprTuple23, 24
23Literal
24Operationoperator: 25
operands: 26
25Literal
26ExprTuple27, 28
27Literal
28Operationoperator: 29
operand: 31
29Literal
30ExprTuple31
31Literal