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Expression of type Less

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.numbers import Abs, Exp, Mod, four, frac, greater, pi, two
from proveit.physics.quantum.QPE import SubIndexed, _alpha, _b_round, _two_pow_t
In [2]:
# build up the expression from sub-expressions
expr = greater(Exp(Abs(SubIndexed(_alpha, [Mod(_b_round, _two_pow_t)])), two), frac(four, Exp(pi, two)))
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|\alpha_{b_{\textit{r}} ~\textup{mod}~ 2^{t}}\right|^{2} > \frac{4}{\pi^{2}}
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)normalreversed('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: 5
operands: 6
4Operationoperator: 23
operands: 7
5Literal
6ExprTuple8, 9
7ExprTuple10, 25
8Literal
9Operationoperator: 23
operands: 11
10Operationoperator: 12
operand: 15
11ExprTuple14, 25
12Literal
13ExprTuple15
14Literal
15Operationoperator: 16
operand: 18
16Literal
17ExprTuple18
18Operationoperator: 19
operands: 20
19Literal
20ExprTuple21, 22
21Literal
22Operationoperator: 23
operands: 24
23Literal
24ExprTuple25, 26
25Literal
26Literal